Gattuso had earlier pushed Jordan in the neck when the two squared up on the sidelines during the game, but after the final whistle he stormed up to the Scot, a former Milan player, and head-butted him.
He was getting increasingly frustrated during the game which Spurs won 1-0.
"I lost my head and I'm taking responsibility because I did something I shouldn't have done," said the fiery midfielder, a former Rangers player.
"Jordan was breaking my balls throughout the second half but that doesn't justify my reaction.
"I was annoyed about the words I'd exchanged with Jordan. We were both speaking Scottish given that I played in his country in Glasgow but I'm not going to say what was said.
"I made a mistake doing what I did to an older person, and that's it.
"I'll wait and see what (UEFA) decides."
Spurs manager Harry Redknapp made light of the incident even joking that Gattuso wouldn't have had much success in a scrap between the pair.
"They lost their heads at the end there - they were rattled for sure - and I guess that's a good sign," he said.
"I know who I'd pick between Joe Jordan and Gennaro Gattuso anyway… Joe all night long. All night long."
Milan coach Massimiliano Allegri admitted he expects Gattuso to be hit with a UEFA sanction.
"At the end of the game it was an unpleasant episode, there was a bit of nervousness, I don't know why it happened," he said.
"I didn't like this episode, it's not nice to see, of course it will be looked at (by UEFA), there was certainly a reason that he behaved this way but you can't excuse it."
Match-winner Peter Crouch joked that Gattuso simply didn't like losing.
Gattuso had also pushed Crouch and grabbed him roughly during the game as he fought a solo running battle with the lanky forward.