Milan's 1-0 home defeat to Spurs in the first leg of their last 16 tie, which began with a whimper as Massimiliano Allegri fielded a defensive team, ended with an explosion of frustration that could lead to a lengthy suspension for Gattuso.
UEFA opened a disciplinary case against him on Wednesday and the Milan captain has already apologised for his "inexcusable" behaviour and said he would accept any punishment coming his way.
"I won't tell you what we said to each other, but we were talking in Scottish," the former Rangers player told reporters after his confrontation with Jordan, an ex-Scotland international who was regarded as one of the game's hard men.
"I lost control. There is no excuse for what I have done.
"Do I expect a ban? I will accept whatever decision."
Milan's focus appears to have been on Serie A from the day they appointed the unheralded Allegri, a former Cagliari boss with no European experience at all, in the close season.
With the mercurial Antonio Cassano and combative Mark van Bommel ineligible having played in the competition already this term for Sampdoria and Bayern Munich, Allegri's hands were tied against a vibrant Tottenham side in pouring rain which epitomised Milan's night.
"We will play a different game. Everything is still possible," he said.
