Montella was speaking in the wake of Roma's 2-2 draw with Parma in the Serie A, where they were at one stage leading comfortably at 2-0 after goals from Francesco Totti and Juan, and looked to be coasting to victory.
However, two goals by Brazilian-born Amauri drew the scores level and cost Roma two valuable points.
Amauri, who is a naturalized-Italian citizen and has been capped by Italy, netted in the 74th and 79th minute to stun onlookers at the Stadio Olimpico, earning Parma a share of the spoils.
Montella has since lamented on his side's inability to see out games, and is keen to address their frequent lapses in concentration at pivotal moments of the game.
Speaking to Skysport, Montella declared: "We concede far too many goals in the final half hour."
"It isn't a question of players or formation but simply a dip in concentration."
"This side has suffered this lapse all season and we must work to put this right."
Montella has also suggested that the tight fixture schedule as the season approaches its climax has made it difficult to immediately address the issue at hand.
"Playing every three days doesn't help when you want to work on weaknesses and of course it will take time."
Nonetheless, despite the dropped points meaning Roma fail to close in on fifth-placed Udinese, Montella was keen to remain optimistic, suggesting there were positives to take out of the game.
"I liked what I saw during the first half and this gives me confidence going forward. After the break we were missing [David] Pizzaro who is fundamental in our particular way of playing."
"It was emotional afternoon for me and we must look to smile despite the fact that we didn't seal all three points."
While Montella's appointment at the helm of Roma is his first venture into management, he will no doubt command the respect of the dressing room, having spent ten successful years at the club, winning the 2000-01 Serie A title, although his finest hour in a Roma jersey is likely to be his four goals in a 5-1 victory over arch-rivals Lazio in 2002.