Rather than be deflated by their recent form, Gattuso remains positive and is targeting a return to winning ways against Sassuolo on Sunday.
With eight games remaining they are far from out of the running and Gattuso has promised his Rossoneri will keep fighting until it is mathematically impossible.
"We still have the same targets," he told a media conference. "We will try to qualify for the Champions League until the end.
"As long as it's mathematically possible, we will keep fighting for all our goals. I do not see why we have to give up.
"We are a young team and we have to play every match with the highest motivation."
To do that, Gattuso has called for greater focus from his squad after being hurt by mistakes earlier in the campaign.
"The team must feel the danger around the corner, the boys need to be aware at all times that an error causes problems," he added.
"We have to improve on this aspect, by working harder, technically and collectively.
"We'll take the initiative tomorrow, but Sassuolo are always dangerous on the counter attack, so we must not lose the ball playing out from the back."
Gattuso's impact since replacing Vincenzo Montella in November earned him a three-year contract earlier this week.
Despite having a deal until 2021, the 40-year-old still knows a run of poor form could see him sacked.
"Nothing has changed since the renewal," said the Milan boss. "In football it takes very little, I lose three games and I'm out of Milanello.
"I feel more desire and more pressure because the club gave me more trust and I'm aware that we still have to improve."