The Italy international has voiced his delight with the Rossoneri's fine run of form and has urged them to keep it going until the end of the season
The San Siro side have endured a difficult 2013-14 campaign and were close to becoming embroiled in a relegation battle earlier in the season, but they have now climbed to joint seventh place in the table after four wins on the bounce.
Milan are back in the race for European qualification following their fine run of form and Montolivo has made it clear they cannot afford to let up with five more games to go.
"We believed in this comeback and day by day the work we are doing is paying off," Montolivo told reporters.
"We can't afford any more slip ups this season, we have to win every game. It will be tough, but we can do it.
"The Europa League is still distant, we can't be making calculations and we have to think only about ourselves.
"It will be tough against Livorno next week, but we have to go for the win."
Milan meet Livorno on Saturday, before taking on Roma, Inter, Atalanta and Sassuolo in their last four games.