The midfielder is looking forward to the second leg of their Champions League tie, and has voiced his satisfaction with the league win over Genoa
The Serie A giants recorded a 2-0 win in the first leg at San Siro, but the midfielder is not convinced that his side will make it to the next round just yet.
"We have to remember how we played in the first leg against Barcelona," Montolivo told the club's official website.
"We’ll have to make sacrifices and show the right spirit. They’re convinced they can win and we just have to play our own game."
Montolivo then went on to voice his delight with Friday's 2-0 league win over Genoa at the Luigi Ferraris.
"It was a tough game and these are three big points. We showed the right spirit and we gave as good as we got.
"We won by suffering. Before Friday we've won by playing well, but to climb high you have to do both of those things."
Milan currently sit third in the Serie A table with 51 points from 28 games.