Gattuso's side had taken a 1-0 lead on the night through Hakan Calhanoglu's stunning long-range strike, cutting the aggregate score to 2-1 in Arsenal's favour.
But six minutes before half-time, Welbeck seemed to go to ground in the area under minimal contact from Ricardo Rodriguez, with referee Jonas Eriksson subsequently pointing to the spot.
Milan never recovered and Arsenal ultimately added further goals from Granit Xhaka and Welbeck in the second half, but Gattuso was keen to not lay the blame entirely at the feet of the referee.
"I don't want to talk about the referee," he told reporters after the match. "We can't find any alibi or [blame] bad luck.
"He [Welbeck] is a striker. He has to do what he does, but we can't use that as entire influence of English football.
"There is a great deal of fair play in English football. I'm not going to judge."
Gattuso cut a frustrated figure on the touchline for most of the match and went as far as throwing the ball towards the face of Arsenal defender Nacho Monreal.
But the pair shook hands soon after and the Italian apologised publicly in his news conference.
"I would like to apologise to Monreal," Gattuso added. "It may have looked like I threw the ball at his face, but that was not my intention."
Although Gattuso generally seemed happy with his team's performance, he was frustrated by the manner of Arsenal's third goal, appearing to accuse his players of giving up after the Gunners' second.
"I'm very upset because in a few years' time we're only going to see 3-1 as the result," Gattuso said.
"When you're on the pitch, you should never give up and concede easy goals. The third goal really upset me. We have to start from the mentality."