The Rossoneri endured a tumultuous early season under Massimiliano Allegri and Seedorf took charge in January in an attempt to arrest their decline and return them to the European places.
The Dutchman failed to fully turn around the club's midtable fortunes, however, and Milan ultimately finished adrift of even the Europa League places in eighth, prompting Seedorf's sacking and former striker Filippo Inzaghi's hiring ahead of the World Cup.
Central midfielder Montolivo, who missed out on Italy's group-stage exit in Brazil after picking up an injury in a pre-tournament friendly, fails to sympathise with Seedorf and believes that getting rid of the former midfielder for Inzaghi was a wise choice.
"With Seedorf, there wasn't much harmony, the decision to sack him was for the good of Milan," he told gathered media at a club publicity event.
"Inzaghi can't wait to get started, though, I felt that even today. He has the right energy to revive Milan and also has the right ideas. It's his first coaching experience but we are all with him, there are all the ingredients here for him to do well."
Montolivo also suggested that the club are attempting to make some moves in the transfer market this summer to bolster Inzaghi's options and claimed the now fully fit Stephan El Shaarawy can be a major success next season.
"The player who can be the biggest surprise is Stephan El Shaarawy, I'm expecting a lot from him. At Milan there are a lot of good midfielders. The club are looking to give Inzaghi a great squad.
"I'm feeling better after my injury - we want to be competitive again and have a great season."