Mulumbu joined the Scottish champions on a free transfer in the summer, but the Congolese midfielder has found first team opportunities hard to come by at Parkhead.
The 32-year-old only made two starts and three appearances for Brendan Rodgers’ side and agreed to return to Rugby Park for the rest of the 2018/19 campaign last month after a chat with his manager.
However, the former West Brom and Norwich City player, who helped Steve Clarke’s side draw 0-0 with Rangers in a William Hill Scottish Cup fifth round match in Ayrshire on Saturday, still feels he can come good at Celtic.
Mulumbu is determined to help Kilmarnock, who are currently in fourth place in the Ladbrokes Premiership, finish as high up the table as possible and increase his chances of featuring for Rodgers’s side next term.
“It was hard at Celtic,” he said. “You are going into a team which is winning every game and you see players like Ryan Chistie, who deserved to play, to get his chance.
“I was frustrated, but I was also happy for Ryan. You could say he took my spot, but he really deserved it and I just tried to stay fit.
“I spoke with the manager at Celtic and he said that, if I could get some games by being on loan, he’d let me go. We are on good terms. I came to Kilmarnock with confidence and a little bit of disappointment. I need to show I’m a good player and that’s what I intend to do.
“Do I regret the move? No, no, no. It’s a great club and my team mates were amazing with me. When I had the chance to play, I was injured and, like I said, Ryan took the spot and we were in the same situation.
“He got the chance and he took it by playing well and scoring in every game. It happens in football. Sometimes you need the luck to be there at the right time and I know things can change quickly.
“I’m here for six months to help Kilmarnock and if I do every right and if we achieve something very good, I know I’ll be back at Celtic in the summer and everything can change from there.
“In my head, it’s not over at Celtic. If you speak with Brendan and the lads, they know I want to go back and do great things for them.”
The midfielder even refused to rule out the possibility of Kilmarnock, who take on Celtic at home on Sunday, from finishing ahead of Celtic in the league this season.
Mulumbu added: “You only understand how great the club (Celtic) is when you sign for them, but my focus right now is entirely on Kilmarnock.
“If we finish first or second, it can change for me. I’m not going to hold back. If we come first, it would be great for us and unlucky for Celtic. What can we achieve? Everything.”
Mulumbu was booed by Rangers fans during the cup tie on Saturday and had a ball thrown at him by one of the travelling supporters in the second-half when he went to retrieve it from the crowd.
“It’s normal,” he said. “I’m a Bhoy! They are going to be on my back, but it’s part of the game. They are against me, but I suppose I have the green fans behind so.”
“I can’t play next week, but I’ll come along and support Kilmarnock, obviously.”