Evergreen AC Milan star Ibrahimovic became the oldest player to score at least 10 goals in the first eight Serie A matchdays, the 39-year-old surpassing Lazio's Silvio Piola (29 years old in 1942-43) for the record.
Ibrahimovic – who struck in the 20th and 54th minutes before hobbling off with injury – also matched Gunnar Nordahl for second-most Serie A goals from the first eight games played of a season by a Milan player, only adrift of Marco Van Basten (12 in 1992-93).
Gattuso played alongside Ibrahimovic at AC Milan between 2010-12 – the pair helping the Rossoneri to their last Scudetto in 2011 – and the former hailed the veteran.
"Milan believe firmly in Ibra, they believe 100 per cent in what they are doing," Gattuso told Sky Sport Italia. "He seems I think even stronger now than he was 10, 12 years ago.
"They put the crosses in because they know he'll get on the end of them. What we did today was create lots of chances and not believe in them fully.
"It's about mentality. Football is about helping each other out, clubbing together, having a kind, reassuring word for your team-mate when they're struggling.
"There are too many people who act like professors, who want to teach you everything. This hurts me."
AC Milan, two points clear of high-flying Sassuolo, have collected at least 20 points from the first eight matchdays for the second time in the three points for a win era – the Italian powerhouse also achieved the feat in 2003-04 as they went on to secure the Scudetto.
Napoli are six points off the pace in sixth position, having lost two of their past three Serie A fixtures and next face Rijeka in Europa League action on Thursday.
Ibrahimovic, meanwhile, is a now a doubt to feature in AC Milan's next Europa League clash against Lille.