St Mirren manager Jim Goodwin felt his team were still struggling from their coronavirus lay-off after being pegged back by Morton in the Renfrewshire derby.
Saints totally dominated the first half and led through Jon Obika's header. But Morton levelled when substitute Ross MacIver headed home following a long throw on the hour mark in Paisley and the visitors had the better chances to win the game.
Saints won the penalty shoot-out 6-5 after the 1-1 draw and moved top of Betfred Cup Group G with progression guaranteed if they beat Queen's Park on Saturday.
Goodwin, whose side had two games postponed last month after a number of positive Covid-19 cases, said: "I thought the first half was excellent, we dominated possession like I would have expected and did everything we spoke about in terms of getting the ball wide and getting balls in the box.
"We had two or three good chances to add to the goal we scored.
"But Morton came out all guns blazing in the second half. They didn't allow us time on the ball and we weren't able to get our heads up and pick out passes.
"And without making too many excuses, I think you saw the fatigue setting in.
"We had a really difficult game here on Friday night against Dundee United and the lads have only had half a dozen sessions in the past four weeks. Fitness levels aren't anywhere near where they need to be.
"We tried to make changes and freshen things up but unfortunately we had lost our rhythm at that point and were kind of hanging on at times.
"Listen, take nothing away from Morton, they were the better team second half.
"But I am glad I am standing here on the right end of the penalty shoot-out, sitting on seven points, and we know what we have to do on Saturday, go there and win the game and if we do that we will go through."
Morton boss David Hopkin said: "We came with a game plan to frustrate St Mirren. We knew Jim has changed his style and was going to be a bit more direct and get balls in the box, and for the majority of the first half we dealt with them.
"We got back in the game and I think over the second half we deserved to win the game. We had two or three really good chances to put the game to bed because we brought more and more forwards on and St Mirren couldn't handle our running off the ball."