The Hoops crashed out of the Champions League with two punishing defeats by Legia Warsaw.
But stand-in captain Mulgrew revealed all their resources would now be poured into ensuring they progress to the group stage of the Europa League and he remains confident they can salvage a season that is already in serious danger of losing its edge.
He said: "The Champions League is where we wanted to be, so we are devastated. But there is still plenty to play for. The season is not over.
"We need to get over this disappointment. That's not easy, but we need to stick together. Potentially, there is still European football there for us. We need to be up for it and keep the season alive."
Mulgrew does not duck away from how poorly the Hoops performed in both games against Legia.
He said: "We never competed well over the two legs and Legia were the better team by far.
"We started well and pressed therm but they never gave us any space in front of their back four.
"They defended well but we can do a lot better. It's devastating. But we have to pick ourselves up quickly.
"We need to work together as a squad, work more with the manager to get his ideas across.
"We know how he wants us to play. We just didn't execute it over the two legs of this tie.
"It just wasn't good enough, no matter what system you are playing. But, we are all reacting well to him, and moving in the right direction.
"The pre-season was geared towards the Champions League. We are not there now but we need to get on with it and be positive."