The Florence-based club have maximum points from two Group K fixtures in the UEFA Europa League.
Despite the ease of their win in Borisov on the scoreboard, Montella said his side were too open at the back and permitted Minsk chances they should not have had.
"It was important to win today and consolidate first place," Montella said.
"We put in a good performance, but allowed far too many chances to the opponents due to a lack of concentration.
"Those are mistakes we should never make and we have got to improve."
Alberto Aquilani opened the scoring for the Italian side, before a six-minute burst just past the hour-mark saw goals to Josip Ilicic and Federico Bernardeschi kill off the contest.
Montella said attacker Bernardeschi, 20, needs to improve, despite scoring two goals in Europe already this term after returning from a season-long loan at Serie B side Crotone.
"He [Bernardeschi] can play as a centre forward, as he showed today, or a support striker," Montella said.
"He needs to improve and we cannot ask for everything right away from a 20-year-old. We must have patience and he is eager to learn."
Montella rued an injury to Micah Richards, which saw the former Manchester City defender subbed off before half-time.
"We wanted a victory today, a clean sheet, a good performance and no injuries," the coach said.
"Unfortunately, Richards needs to be evaluated, as he had a muscular problem that he's suffered from in the past."
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