After their FA Cup exit at the hands of non-league Lincoln City, he said "if the club want to sack me, so be it".
But now Town are unbeaten in five games, having drawn 1-1 at Carrow Road in the Championship on Sunday.
"I would hope that performance and result goes a long way to repairing our relationship with the fans," he said.
"It's been broken at times. They've not enjoyed it, they've not been watching good, attractive, winning football. I get that, I've not been enjoying it particularly.
"So over the last five games I think they've seen us play really well, and I would think helping stop Norwich in their tracks during a promotion push will endear us to our fans a little bit more."
McCarthy's side are currently 15th in the Championship, 11 points above the relegation zone and 16 behind the play-off places.
Jonas Knudsen opened the scoring for Town at the home of their fierce rivals, only for the eighth-placed Canaries to draw level after Jacob Murphy's shot squirmed through Bartosz Bialkowski.
But Town's Polish goalkeeper pulled off a string of fine saves in a man-of-the-match performance, and McCarthy believes Bialkowski is the best in the division.
"In my mind I haven't seen anybody better. He's outstanding," McCarthy told BBC Radio Suffolk.
"He's kept them out, he's been brilliant and he's let the one in. It happens, but what was good was we didn't concede again, and maybe eight weeks ago we would have lost that game."
Murphy's goal was his ninth of the season, but the midfielder said he took inspiration from Nathan Redmond's goal against Ipswich for Norwich in the 2015 Championship play-off semi-final.
"I'd watched the goals from the previous games and Nathan scored a similar one two seasons ago at his near post," he told BBC Radio Norfolk.
"So I knew that he would be vulnerable there. That was the thought process with that. You've got to exploit weaknesses."
Ipswich Town boss Mick McCarthy hopes his side's performance in the East Anglian derby at Norwich will help mend a "broken" relationship with the fans.