The 27-year old was perfectly placed to head home Kris Commons' corner midway through the second half but nodded wide of the mark.
Minutes later, ten-man Celtic conceded to Cesc Fabregas prompting Mulgrew to really rue what could have been for he and his teammates.
"It was an unbelievable chance," Mulgrew told ITV. "You can see that on the TV. I should have scored."
Mulgrew added: "It's hard to go down to 10 men so early in the second half. It was always going to be an uphill battle.
"I thought we defended really well and had a few chances. If we'd have taken them it would have been different."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball