A Paulo Dybala strike gave the Old Lady the lead before former Juve defender and current Milan star Leonardo Bonucci levelled things up.
Late strikes from Juan Cuadrado and Sami Khedira ensured Juventus moved four points clear of Napoli, while Milan are now eight points behind Inter in the race for Champions League qualification.
Gattuso told Mediaset Premium as quoted by Football Italia: “The performance remains, it felt a bit like the (Europa League defeat to Arsenal) in London. The result doesn’t reflect the performance, but we have to get back on our feet.”
The former Italy midfielder also criticised Hakan Calhanoglu because of the Turkey international's penchant for arguing with his teammates.
Gattuso added: “I got angry with Calhanoglu at one point because when he loses the ball, he starts arguing. I don’t like to see that. He looks at the ground, starts shouting at his teammates. If he just lifted his butt off the ground and got running after the ball to win it back, we wouldn’t concede the second goal.
“We put in a good team performance and we didn’t win, which means we’ve got much to improve.”
Milan face Inter on Wednesday, looking to reduce the eight-point gap that emerged on Saturday after their San Siro rivals beat Verona 3-0.
Gattuso added: “Up until three months ago, it was unthinkable that we could challenge for a Champions League spot, so we must recover our energy and keep taking it one game at a time.
It's a bitter result but we're proud of you, boys! You fought well and we deserved more! 🔴⚫️ Now let's give it our all against Inter! 👊🏻 #weareacmilan— AC Milan (@acmilan) March 31, 2018
Un risultato amaro ma siamo fieri di voi! Avete combattuto e meritavamo di più! Adesso testa a #MilanInter 💪🏻#weareateam pic.twitter.com/V8ZnE0netl
“We have quality players, but in physical terms we cannot compete with Juventus. That is what made the difference today.
“It was a good performance, fine, but I can’t be satisfied with that when all that remains is the 3-1 result in the record books. Nobody will remember the performance.
“It burns, I can’t stand here and smile or pretend I’m happy with just playing well. It burns me and it has to burn everyone, otherwise nobody will become a champion if they’re content with this.”