Sevilla has three wins in a row entering the first leg on Wednesday, but Montella is not happy with the many chances wasted on attack.
And they can't afford to be inefficient against the English Premier League's best defence.
"We need to be capable of finishing off the chances we create," Montella said after Sevilla beat Las Palmas 2-1 in the Spanish league on Saturday. "We had six, seven, eight opportunities to score and we didn't. I'm not happy with that."
"We must be able to capitalize on our chances because games can change in a second," Montella said. "I liked the team's spirit, but we need to improve technically and we need to score more."
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Jose Mourinho's United has conceded 19 goals in 27 Premier League matches, better even than runaway leader Manchester City.
Sevilla has a respectable attack which last month was boosted by the signing of former Barcelona forward Sandro Ramirez. Montella has options in attack, including Luis Muriel, Nolito, and Wissam Ben Yedder. His attacking midfielders include Pablo Sarabia, Jesus Navas and Joaquin Correa.
"I studied him as I was beginning as a coach," the 43-year-old Italian coach says. "It's gratifying to prepare for matches like these. Not because you can defeat Mourinho, but because it's a huge match."
Sevilla, a five-time Europa League winner, is trying to advance past the round of 16 of the Champions League for the first time. It was eliminated by Leicester City at this stage last year.
United, the defending Europa League champion, is back in the last 16 of the Champions League for the first time since 2014.
"We are not afraid of United," Sevilla defender Clement Lenglet says. "They have a lot of quality but we do as well. We will have to play at a very high level to score against a team that concedes very few goals. We can be motivated by the fact that not a lot of people think that we will advance. We want to show that we can compete against any team."