But, the defender is adamant the Hoops will have their mojo back for Saturday's home match against Europe-spot-chasing Inverness.
The Scotland star said: "It's very hard to do and it plays on your mind for a few days. But, we need to put the result behind us and move towards the next match."
Manager Neil Lennon has made no attempt to disguise his pride in what his players have already achieved this season.
Nor did the Hoops boss try to hide the fact he is convinced referee Craig Thomson's decision to send off Virgil van Dijk, then not award a penalty against the Dons when the ball struck the right arm of Mark Reynolds as Celtic piled on the pressure in the second half, had huge implications on the final result.
Lennon said: "I didn't think it was a sending off. I thought it was an awful decision, and it was quite clear we should have had a penalty for a hand ball in the second half.
"Along the way, you are always thinking it might be something like that [the decisions] that breaks the run."
While Lennon must now wait to see if his comments bring any reaction from SFA compliance officer, Vincent Lunny, Mulgrew revealed the manager was even more vocal when addressing his side at half-time at Pittodrie.
And they were words which the man who had to step back into central defence when van Dijk departed recognised.
Lennon used an equally motivating speech at Rugby Park in his first season in charge when his side trailed by three goals at the break and fought back to 3-3.
Mulgrew explained: "It was a similar situation when we were 3-0 down at Kilmarnock a few years back.
"He said a lot of similar things then and he gave us a lot of belief.
"He does that, and maybe on another day we might have gone on and got a result out of it."
On reflection, Mulgrew believes Celtic did enough to maintain their proud, unbeaten record, but lacked the little bit of luck required on the night to deny their second victory over the league leaders in the past month.
"The sending off changed the game," Mulgrew told Celtic TV.
"It was disappointing to get a man sent off, then they scored a great goal that you can't do anything about.
"But, we were disappointed the way we lost the second goal, and it was about how we reacted in the second half.
"We only had 10 men, but it was just waves of attack as we went all out for it.
"We got the first goal at a good time but we just couldn't get the break for the second."