Gonzalo Higuain's first Rossoneri goal salvaged a draw at Sardegna Arena on Sunday, cancelling out Joao Pedro's early opener on the midfielder's return from a doping ban.
Suso forced two saves from Alessio Cragno in the closing stages, while Higuain headed a Diego Laxalt cross wide, but Gattuso was furious at his side's first-half display.
"The start we have had is a problem that we have to solve," Gattuso told Sky Sport Italia.
"The first 20 minutes were embarrassing. If you go down 2-0 in this game we cannot recover it anymore.
"We did a lot of good, but in those 20 minutes it was a very bad game on the mental level, tactical, over everything.
"I did not see any offensive insertion in the first half hour, that's not good enough. The road is still long, today we went well."
Milan have a game in hand over leaders Juventus but sit eight points off the pace after their opening three fixtures, leading Gattuso to mock pundits who suggest they could rival the Bianconeri.
"I laugh when people say that we are the second or third best team," he added.
"Our potential is strong, but if we do not win these games it becomes tough.
"I do not want to throw my hands in the air, but there is still a long way to go. If we can learn to manage certain situations we can have an important season.
"If you want to be a contender for a championship you cannot afford to have an attitude like this - and this happened last year."