And the Light Blues skipper said he was pleased for Ally McCoist because of the flak the manager took following the 1-1 draw with Albion Rovers in the Scottish Cup quarter-final at Ibrox on Sunday.
McCulloch said: "I am delighted we have done it with eight league games to go. It is a fantastic feeling. I thought we played really well. Fair play to Airdrie, they came out and had a go by playing two players up front.
"To go 28 games, and win 26 and draw just two is brilliant. It's a fantastic record and is something we want to keep going.
"Saturday's game against Dunfermline is really important now.
"It was unreal to get a hat-trick. Two of them were penalties but I was delighted to see the third one go in.
"The most important thing was getting the win and the three points. It was a great win for the manager. I was delighted we could give him and the fans something to shout about. They deserve it more than anybody.
"It was great to repay the manager for the faith he has shown in the boys by getting his second league title wrapped up."