Connor has yet to taste victory since taking over following Mick McCarthy's departure in February, losing eight of his 10 games in charge.
But Rodgers said: "Terry has done a terrific job there, he was really thrown in at the deep end and has handled himself admirably and he is a guy who deserves a chance going forward believes with that job.
"He has done remarkably well in relation to steadying the ship but unfortunately he hasn't been able to help them stay up, but he is someone who deserves the chance to get the club back up there.
"He has been there a long time and he knows the soul of the club.
"I think everyone would agree, looking at the sacking of Mick, that it was something that did not make sense, especially after the event where there was maybe no plan in place to put someone else in.
"Terry has come in and stepped forward and I believe if given the chance he has every chance of taking the club back up again.
"They have been around for a little while at this level and they have the infrastructure in place to jump up again."