Leigh Griffiths scored the only goal of the game in the 84th minute as the Hoops finally broke down a stubborn Saints rearguard.

But while the Celtic manager had praise for his goalscorer he slammed centre-back Boyata for a straight red card after the Belgian international went too far in questioning referee John Beaton’s decision not to award him a foul.

“It is a stupid red card. He has got enough opportunities to not get sent off. It was a very emotional game towards the end.

Brendan Rodgers was relieved his side won in Perth but he hit out at Dedryck Boyata for a 'stupid' red card. Picture: SNS Group

“Dedryck feels as if he should have got a free-kick and didn’t get it,” said Rodgers, who admitted it could leave him short for the semi-final after Kristoffer Ajer was forced off with a hamstring pull.

“In fairness to John [Beaton], he gives him a chance not to get the red card. It’s not what we would want, but we move on.”

The Parkhead boss also conceded that the SPFL could have a serious scheduling issue on their hands, after the semi final draw paired Celtic with Hearts and Aberdeen with Rangers.

Hampden will not be able to accommodate the semi-finals, both of which will need to be played on Sunday October 28.

There would appear no other suitable date since the Glasgow clubs have Europa League fixtures on the previous Thursday and a full Premiership card is scheduled for the following midweek.

One of the semi-finals could end up being switched to the Monday, but the situation could bring Murrayfield into play.

Police will almost certainly refuse to sanction Celtic and Rangers playing in Glasgow on the same day through utilising one of their stadia alongside Hampden.

“I think they will have to look at it now,” Rodgers conceded. “It obviously presents a problem because there are midweek games the week after. I’ll let them sort that out.”

Rodgers cut a relieved figure as his team bounced back from their Kilmarnock defeat to secure passage to the last four thanks to the late goal from Griffiths - the Scotland forward’s third in as many games.

Rodgers was keen to move on from the revelation that he turned down a “serious offer” from China in the summer, meanwhile, which he acknowledged had come via a formal approach.

“Since I’ve been at Celtic the last couple of years, I’ve had a few offers,” he said.

“That’s no different to any of the others. My focus is very much on Celtic and being here, helping us rise to the challenge of this season. There’s nothing more really to say on that.’

Pressed on interest from China and what consideration he had given to it, Rodgers said: ‘What you know with China is that it’s an awful lot of money.  “But I’ve found happiness here and I spoke with the owners of the club and the board and we found an agreement and we move on.  “I’ve had other opportunities, but I’ve still got this year and another two years on my contract and unless they get fed up with me or something else happens I’m very privileged to be here.’

Rodgers, who said the meeting with Hearts made for “a tough draw” that the identity of the semi-finalists meant his team were “always” destined to be handed, expressed contentment at his team getting the job done after stepping up their tempo and pressure on the home goal in the second period.

“I think we could have decided the game a lot earlier than what we did. We had a slow start. We had a lot of possession, but weren’t dangerous enough, which we would prefer.  “But we still created two really good chances in the first-half and didn’t take them. It was just a case of trying to tire St Johnstone out.  “More of the same in the second-half. We continued to create opportunities. As long as you take one and don’t concede up the other end. It was a really good finish by Leigh.  “He made a good run to the first post, it has gone beyond him, but he checked back out, was alive and alert and produced a very good finish.

“Leigh could have had a hat-trick, but what is important is that he is smelling the goals again. He is making the right moves.  “He had a couple of great opportunities getting into good positions and credit to their keeper as he made a couple of great blocks.  “Leigh is always going to be alive in the box for chances coming and it was a great finish.”

Brendan Rodgers slams '˜stupid' red card for Dedryck Boyata