Franck Kessie's 79th-minute penalty sealed a first victory in five attempts for the Rossoneri, moving them back into fourth place and landing a significant blow against Lazio's own Champions League qualification ambitions.
Tensions then boiled over, with Lazio defender Luiz Felipe and Milan winger Fabio Borini seemingly at the centre of a post-match brawl.
A famously combative presence during his playing days, it was a flashpoint Gattuso conceded he would have once relished.
"When I was a footballer I was the master of these situations. They excited me," he told DAZN.
"I have a different role now, I see things differently. Also, I am too old. These are guys who go to the gym every day. I am not as strong as I used to be!"
Another element to the post-match hostilities was the on-going spat between Tiemoue Bakayoko and Francesco Acerbi.
Milan midfielder Bakayoko engaged in some back-and-forth with Acerbi before the match as the Lazio defender insisted his team were, "stronger – there is no comparison" and the Chelsea loanee retorted, "Okay, I'll see you on Sunday."
Bakayoko swapped shirts with Acerbi in what appeared an antidote to the immediate post-match chaos, but he and Kessie then held their opponent's jersey aloft to the home fans at San Siro.
Acerbi posted a picture of Kessie and Bakayoko's celebration on Instagram afterwards, with the caption: "I'm sorry because I exchanged the shirt to put an end to the matter, fomenting hatred is not sport but a sign of weakness."
It combined to take attention away from a fine performance from Milan, who were second best during a thrilling, end-to-end first half but managed to impose their will on the contest after the break.
"You have to give it your all when you play against Lazio," Gattuso added. "You have to be quick, strong and smart.
"The players have to fight for these colours. We had to put up a strong performance and we did, so I am pleased.
"I want to send my congratulations to the lads on a job well done."
Gattuso confirmed his captain Alessio Romagnoli was substituted due to a thigh injury.