The AC Milan skipper is disappointed after Clarence Seedorf's side failed to secure a top-six finish, despite a win against Sassuolo
Milan went into the final day of the season with a mathematical chance of securing a top-six finish and though they beat Sassuolo 2-1, Parma and Torino's results saw them finish eighth.
"There is a lot of regret that we didn't qualify for the Europa League, we're not hiding that," he told Mediaset Premium.
"In the final game of the season, we tried to get into Europe, but the standings were already compromised."
Montolivo was keen to avoid questions concerning the future of Clarence Seedorf and is shifting his attention to Italy's World Cup campaign.
"It's not up to me to talk about Seedorf's future. We did well with him and tried to redeem ourselves. Now I'm thinking about the World Cup, I hope it can be magical for Italy."
Goals from Nigel de Jong and Sulley Muntari gave Milan victory at San Siro but the Rossoneri later had two men sent off.