With some improved performances in their last two outings - a 1-1 Europa League draw with Rennes away and a hard-fought 2-1 win over Aberdeen in the domestic league - Mulgrew feels the tide is starting to turn at Parkhead and hopes things can become more positive for Lennon and his men.
"The manager has shown faith in a lot of boys here and everybody wants to win the title for him," the 25-year old said.
"We are all right behind him and working to repay his faith.
"We feel we owe him so everybody is concentrating on doing the club and the manager a turn.
"I keep saying we need to go on a run and hopefully this can be the start. There have been a few positives in the last week and we need to push on from here.
"I was delighted to get the winner against Aberdeen although I haven't scored many right-footed goals, that's for sure.
"There was a lot of relief when it hit the net and it was good to get the goal and the three points.
"I wasn't thinking that we hadn't won in our last four games. I just knew we needed a result to start a run.
"Obviously you want a performance to go with it but the main thing is that we won."