McGowan limped off after Conor Newton had given Saints the lead and the Championship side twice levelled to force a second meeting at St Mirren Park on 10 December.
Lennon said: "Gowser picked up a knock in training but decided he couldn't go on after a quarter of an hour and asked to be subbed.
"We actually missed the wee man when he came off but I have to respect his honesty as he put the team first.
"He would not have been his usual busy self if he had stayed on but it was an important point in the match.
"I'm a wee bit disappointed that we got ourselves in front twice but didn't hold on to it for a prolonged period of time.
"That is all down to an energetic Queen of the South side. It was a proper cup tie. It wasn't great football played by either side but both sets of fans were thoroughly entertained."
Queens boss Jim McIntyre said: "I thought my side were excellent. It was a difficult start losing the early goal and St Mirren had us rattled.
"But after 20 minutes we started to make some passes and looked a real threat.
"As for the replay, we've got a chance. It will be difficult again - they are a Premiership side - and we will need to be at our maximum once again, but that is what we will aim to do."