Neil Lennon's side will clinch their third successive top flight crown in a matter of weeks but crashed out of the League Cup and Scottish Cup to Morton and Aberdeen respectively and came up short in the Champions League against Barcelona, Ajax and AC Milan.
And Mulgrew reckons a sense of realism is needed when assessing their campaign.
He said: "Yes, it has been a successful season.
"We got into the Champions League and we qualified again via three qualifiers.
"I know it is forgotten now because we're not in it any more but the group we were in was always going to be hard and the expectation was more because we had qualified the year before.
"It was an achievement getting in there. Obviously, cup competitions have been disappointing but we've done really well in the league so far and are unbeaten.
"We'll assess it at the end of the season but hopefully we can continue our form in the league.
"People are quick to forget we did qualify for the Champions League.
"I know there were one or two bad performances but we got there in the end.
"The year before people were saying it was an achievement just to get in there but then once we got in and qualified for the last 16, expectations were raised again.
"What would have been good enough this year? The quarter-finals?
"It was a harder group, it was always going to be difficult with the money teams are spending in comparison to what we're spending."
Celtic return to Premiership action against St Johnstone tomorrow and are now just 14 games away from completing an unbeaten campaign.
"People are starting to talk a lot more about it now," Mulgrew said.
"I don't like thinking about it too much. But the managers and others are speaking about it so it's an aim for this season."