The Rossoneri ground out a 2-1 victory at San Siro in a clash which saw Lucas Paqueta dismissed for slapping the referee's arm, while Gattuso visibly argued with Tiemoue Bakayoko on the sidelines over his substitutions.
It emerged afterwards that Gattuso was unhappy with the amount of time it took Bakayoko to prepare himself when asked to warm up, although the on-loan Chelsea man refuted that he was ready to give it "200 per cent".
Bakayoko now looks unlikely to return to San Siro on a permanent basis next term.
Gattuso is now keen to move on from the incidents ahead of his side's trip to face Fiorentina on Saturday.
"I'm sorry that the victory has been overshadowed," he said at a news conference.
"There has been more talk of Bakayoko. Tomorrow we will need a great game, if we do things well we can put them in difficulty.
"We must think of ourselves. We haven't won away at Fiorentina since 2014. Up front, they have great players, and they can cause trouble for you."
Despite the fallout from the incident with Bakayoko, Gattuso insists that he will not let it affect his team selection.
"Tomorrow you will see the team I have picked," he added.
"Consistency is the most important thing, but you always put the club first. I have never held a grudge, same goes for the players.
"[Lucas] Biglia is called up, but he is not available. [Lucas] Paqueta has been training well even if he is disqualified. [Hakan] Calhanoglu has trained and is available."
Roma are also level on points with the Rossoneri going into the last three games of the season, although it was announced on Friday morning that Claudio Ranieri will depart the Italian capital at the end of the campaign.