Gattuso cut a frustrated figure during Milan's 1-0 defeat to Tottenham at the San Siro and regularly squared up to beanpole striker Peter Crouch after challenges between the pair.
He also argued with Spurs' assistant manager Joe Jordan on the touchline before pushing the former Milan player in the neck. And after the game he ran over to confront Jordan again before head-butting the 59-year-old.
Gattuso came out afterwards to apologise but he is expected to receive a minimum three-game ban, possibly more.
However, Galliani says everyone has been too quick to condemn the club vice-captain.
"What Rino (Gattuso) did is a regrettable incident which isn't right but he was seriously provoked," said Galliani.
"Of course he shouldn't react in this way but don't stigmatise everything.
"Gattuso has played 104 matches in Europe and was only sent off once in 2003 after hitting (Zlatan) Ibrahimovic, hence a clash between two future team-mates.
"We'll present our defence tomorrow (Friday) and ask (UEFA) to take into account Gattuso's behaviour in 104 matches, then we'll see what to do after the sentence."
Gattuso would have been suspended for the second leg in London anyway after picking up a booking for a poor challenge on Steven Pienaar.
"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, after the game.
"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."
Milan coach Massimiliano Allegri admitted he was disappointed with his player.
"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," he said.
Tottenham boss Harry Redknapp was unperturbed, though, and even joked that Gattuso had bitten off more than he could chew in challenging former midfield hardman Jordan.
"I know who I'd pick between Joe Jordan and Gennaro Gattuso anyway... Joe all night long. All night long," said Redknapp.