Celtic manager Martin O'Neill tells BBC Scotland: "Delighted to win the game. The exertions and disappointment of Tuesday night, have to overcome that and travel back.

"The physical and psychological aspects of it all were big concerns today. Falkirk caused us umpteen problems in the game here last season.

"We created a lot of really good chances, but at 2-0 it's still on a knife edge. They get the goal and then the last 15 minutes become a worrying time when perhaps it shouldn't have been.

"We go again on Wednesday and we'll see how the players are. A lot of the players that played on Tuesday started to flag a little bit and it's early season - the players are still getting up to speed."

Image source, SNS

St Johnstone head coach Simo Valakari tells BBC Scotland: "We created enough chances, but if you don't take them, it's hard to win and we didn't. That's the disappointment.

"I like how we played, our players wanted to show themselves. When we found our rhythm, the boys really played, but it's all about the result and we did not get it.

"The belief was there, it took us 15-20 minutes to find the spaces and, even first half, we had our chances. We stepped up pressure in the second half and had more turnovers higher up the field.

"When we do that, we're a very good team and we created a lot of very good moments there."

Image source, SNS

Dundee United assistant manager Lee Sharp tells BBC Scotland: "Really pleasing. Probably one of the most pleasing things was the fact that we got a clean sheet.

"Defensively, we were excellent. To create so many chances and score the four goals and to have another few chances we should've put away, all in all it was really, really pleasing.

"To a man, we were excellent all over the park. Will [Ferry] was excellent. I don't know what he's doing cutting in on to his right foot and shooting from there. It's some hit. It's some goal. And his delivery for the fourth one's exceptional."

As for absent manager Jim Goodwin, Sharp adds: "He was delighted, he was delighted. He managed to have a chuckle. He was over the moon for the team as well."

Image source, SNS

Allan Preston
Former Hearts player on BBC Sportsound

Even this early on in the season, if you're a Hearts fan, it's great to come and watch them.

They can't defend, they concede goals, as we've seen again today, but they score. They've got so many attacking threats.

Image source, SNS

Elgin go top of the fourth tier with an emphatic four-goal win over Stirling after Clyde are made to pay for Logan Dunachie's 60th-minute red card.

The Bully Wee were 3-0 up away to Spartans but were pegged back and had to settle for a point - and are now a point behind Elgin.

Stranraer are up to fourth after beating Kelty, while Dumbarton are bottom, behind Edinburgh on goal difference, after losing in Annan.

Hamilton have moved four points clear at the top of the third tier after a narrow win over Cove.

However, Ross County have two games in hand and can narrow that gap when they host East Kilbride in a match being shown live shortly on BBC Alba.

Alloa have moved a point above Kilby into third with their draw at home to Peterhead.

Airdrieonians remain without a win after a goalless draw at home to East Fife, while Queen of the South remain without a point at the bottom after losing in Montrose.

Part-timers Stenhousemuir continue to surprise and are now out on their own, two points clear at the top of the second tier after beating Caley Thistle - the same team who beat them to the League 1 title.

Stenny benefit from second-top Partick Thistle being held to a draw at home to Glasgow rivals Queen's Park.

The latter stay bottom as Morton also secured their first point with a draw in Ayr, while Arbroath leapfrog visitors Livingston into fourth with their one-goal victory.

That's champions Celtic three points clear at the top of the Premiership, with Hearts ahead of Dundee and St Mirren, who play tomorrow, on goal difference.

Dundee United are up to sixth but have played two more games than the teams around them.

Stay with us for reaction from the managers at all three Premiership games.

Celtic have won their past 10 games in the Premiership, their most recent longer winning streak was from 13 April 2024 to 6 October 2024, a run of 13 games.

Falkirk have failed to win in their past six games in the Premiership, their longest winless streak in the competition since at least 2013-2014.

• Annan Athletic 2-0 Dumbarton

• Elgin City 4-0 Stirling Albion
• Spartans 3-3 Clyde
• Stranraer 2-0 Kelty Hearts

Martin Dowden
BBC Sport Scotland at Celtic Park

Camilo Duran made the difference in the end, but this was far more uncomfortable for Celtic than it might have been.

Having a two-goal cushion at the break, most would expect them to add to that, but a combination of a good Falkirk side and lack of verve contributed to a degree of doubt over the outcome.

Job done for Celtic, which was a must after their Champions League exit.

Maximum Premiership points, but not as routine as appeared likely at one stage.

• Airdrieonians 0-0 East Fife
• Alloa Athletic 1-1 Peterhead
• Hamilton Academical 1-0 Cove Rangers
• Montrose 2-1 Queen of the South
• Ross County v East Kilbride (17:30, live on BBC Alba)

• Arbroath 1-0 Livingston
• Ayr United 1-1 Greenock Morton
• Partick Thistle 0-0 Queen's Park
• Stenhousemuir 3-1 Inverness Caledonian Thistle

It was far nervier than most would have thought when Hearts raced into a two-goal lead, but credit to St Johnstone who fought all the way.

James Wilson's strike in the ninth-minute, plus Enes Alic's own goal, prove to be enough for Wouter Vrancken's side.

But Hearts really tired in the second half and St Johnstone almost took full advantage, scoring through Rauri Paton and going close on numerous occasions.

Image source, SNS

United secure their first Premiership win of the season and provide some cheer for absent and unwell manager Jim Goodwin.

Emmanuel Agyei, Zac Sapsford (with a penalty) and Will Ferry put them firmly in control in the first half and Jesse Randall added another after the break.

That's three defeats out of three for Kilmarnock in the Premiership and two by a margin of four goals at Rugby Park.

Image source, SNS

A deserved win for Celtic, thanks to Camilo Duran's first-half double, but they didn't make it easy for themselves.

Several missed chances for the hosts and Colby Donovan's own goal made it a nervy finish, but they see it through for all three points.

After Tuesday's dismal showing, a win was much needed for Martin O'Neill's side.

Image source, SNS

Only two minutes of added time at Celtic Park.

Claudio Braga almost seals all three points for Hearts as the forward curls from 25 yards out, but it's just over the over the bar.

The Portuguese has been quiet by his usual high standards.