Montella, the first coach to go since former Italian Prime Minster Silvio Berlusconi sold the club to a Chinese-led consortium in a 740 million-euro deal in April, had been in charge since the start of last season when he led Milan to sixth place in Serie A.
"In these situations, the coach is always to blame and that's fair enough," Montella told reporters as he left Milan's training ground.
"Expectations were raised a bit too high by everyone in the summer.... I'm very sorry because I know that the players were behind me. They deserve much more and I'm sure they will make it out of this difficult phase."
Gattuso, 39, spent 12 seasons playing for Milan, winning two Serie A and two Champions League titles plus the Club World Cup, and was known as one of Italy's toughest players.
His coaching career has been a mixed bag, although never dull.
He began at Swiss first division side Sion in 2013 but was sacked after three months before joining Italian Serie B club Palermo who fired him after six games.
In 2014, he tried his luck with Greek Super League side OFI Crete who were beset by financial problems and, according to Gattuso, were "struggling to feed their players".
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He lasted six months, during which he gave an infamous expletive-ridden news conference in which he banged his fist on the table repeatedly and said, in broken English, that he expected his players to "play with balls".
He moved to Pisa in the third tier of Italian football, won promotion to Serie B at the first attempt in 2015-16 only for them to go straight back down the following season, with Gattuso still in charge, amid administrative and financial problems.
Milan, 18-times Italian champions, enjoyed a golden age under Berlusconi but his last few years as president became a story of unsuccessful transfers, mid-table finishes and musical chairs in the coach's seat.
Chinese ownership heralded a change of direction symbolised by the decision to spend about 40 million euros to sign experienced Italy defender Leonardo Bonucci from champions Juventus.
Younger recruits included Portuguese striker Andre Silva, right back Andrea Conti, a product of Atalanta's impressive youth scheme, Switzerland left back Ricardo Rodriguez and Turkish midfielder and free kick specialist Hakan Calhanoglu.
The new-found optimism was apparent at Milan's first home match of the season when a 65,000-crowd turned up at San Siro on a stifling August evening for a Europa League tie against modest Romanian side Universitatea Craiova.
Milan, seven-times European champions, won their first six competitive games but quickly lost their spark and Sunday’s match was their fourth home league game in a row without scoring.
(Reporting by Brian Homewood in Basel, editing by Ed Osmond and Ken Ferris)
