The Rossoneri were grateful to a superb Gianluigi Donnarumma save from Arkadiusz Milik in stoppage-time to earn a point against Maurizio Sarri's men.
"In the last four matches, we have faced Juventus and Napoli and we are still far from them," Gattuso told Milan TV.
"However, we stood up, played offensive football and took our risks against them, which is positive.
"Suso and [Hakan] Calhanoglu worked hard to close their spaces making it difficult for them to pass the ball forward.
"Sometimes I ask my attacking players too much. We played well but we still have to raise the bar."
5 - The number of draws nil-nil in the 32 Serie A 2017/18 match-day, a joint-record in a single MD in the 3 points for a win era. Weight.— OptaPaolo (@OptaPaolo) April 15, 2018
With Napoli having won just two of their last six Serie A games, holders Juve opened up a six-point lead atop the table with a 3-0 defeat of Sampdoria.
But Sarri is not worrying about Juve's results although Massimiliano Allegri's men appear to be closing in on a seventh consecutive Scudetto.
"We don't care what Juventus do," Sarri told Mediaset Premium. "We are on our journey, the team did well.
"If we had played this performance with this result in the first half of the season, we would have been praised for it.
"The only regret is that if we had played against Sassuolo [a 1-1 draw last month] with this determination, we would have more points.
"Aside from a couple of crosses, we allowed Milan absolutely nothing."