Brendan Rodgers congratulates matchwinner Leigh Griffiths in Perth
Celtic's League Cup quarter-final win at St Johnstone was "psychologically good" for the holders, says manager Brendan Rodgers.
Leigh Griffiths scored the only goal to set up a semi-final against Hearts for Rodgers' side, who have had their worst start to a league season since 1998.
Defender Dedryck Boyata was sent off late on for Celtic, who lost to Kilmarnock on Sunday.
"What's most important tonight is to get through," said Rodgers.
"We scored one and could've had maybe one or two more. The keeper's made some fantastic saves but we got ourselves in the next round so I'm very pleased.
"Psychologically, it's a very good win for us. We're into the semi-finals. Whoever you get, it's always going to be a tough game."
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With Rangers drawn to face Aberdeen in the other semi-final, there is doubt over where and when the ties will be played.
The games had been scheduled to take place at Hampden on 27 and 28 October, but both Celtic and Rangers have to play on the Sunday due to their Europa League commitments on 25 October.
Police are unlikely to permit both matches to be played in Glasgow on the same day.
"We've enjoyed the last couple of years at Hampden and let's hope we enjoy it this year as well," added Rodgers, who has never lost a Scottish domestic cup tie.
Celtic created plenty - analysis
Former St Johnstone forward Billy Dodds on Sportsound
Celtic deserved to win the game. They created glorious chances. They were pushing, they were much better second half. They got the ball forward quickly and that's what helped Celtic. You've got to feel for St Johnstone. They defended well. They kept going at it.
Former Celtic midfielder Paul Hartley on Sportsound
It's been a real struggle for them in front of goals and they've not created a lot of chances. But tonight I thought they created good chances. They'll take the result, they're through 1-0 and it's a clean sheet.
Source: bbc.com