But the Celtic stopper also made it clear there is no need for anyone to hit the panic button over the 1-0 home loss to Inverness Caley last weekend.
Parkhead manager Neil Lennon was involved in a spat with a couple of supporters who were criticising the team, prompting him to threaten to quit if the fans no longer wanted him at the helm.
Although that most certainly isn't the case, it has increased the pressure on them going into tomorrow night's showdown with Hearts at Tynecastle.
Mulgrew has been around the block enough to know the expectation levels when you play for Celtic, and says the last thing his team-mates would do is use European commitments as a reason for not picking up enough points in the league.
He said: "There's been a lot of games, but you want to be involved in as many as you can and at the highest level you can. When you're in the Champions League, there's no complaining that there's too many games. We've got a big enough squad to cope and we're enjoying it.
"It's demanding. Against Barcelona a lot went into the defensive side of it, but it's where we want to be and we're not complaining.
"It might be a factor (contributing to domestic results), but I'm not using it as an excuse. On Saturday we never took our chances. It's that simple. If we did, it might have been a comfortable day for us. We know we have to improve upon that. It just wasn't good enough.
"But Hearts will be pumped up tomorrow night and so will we. It's a great atmosphere there and one we're looking forward to playing in."
Mulgrew also made it clear the Celtic players don't believe they will open up a huge gap in the title race as soon as they no longer have Champions League qualification to focus on, as has been suggested in some quarters.
He said: "Of course there is a title race. It's only people on the outside who are saying there won't be one. No-one's saying it in the changing room. We know it's going to be difficult.
"I also don't believe we are lacking an edge because there is no Rangers. I think you still have to play the same teams. It's still the same games whether Rangers are there or not. We need to focus on what we're doing. And we need to win the games."
Mulgrew also insisted Lennon's confrontation with a few fans shouldn't develop into something it isn't.
He added: "It's one of those things in the heat of the moment when the game is not going our way. Fans have a right to have an opinion – the way it was going we just didn't take our chances.
"They're entitled to their opinion and the manager got a wee bit heated. It's just one of these things that happen. We are all in it together with the fans."