Sevilla host United on Wednesday night in the first-leg of their Champions League round 16 tie.
"We have to be better than against Atletico," said Montella.
"Now we have more experience and some months working together. I hope that tomorrow is played with less emotion but with the same spirit as always.
"I'm happy with the team's performance but it can be improved.
"I am very excited about tomorrow's game, it will be difficult, tough, we have to be physically and mentally strong, and we have to trust the players.
"We have to play with experience and with the head, but we also have to play with desire."
Alexis is eligible to appear for his new club in the tie and Montella has watched the player's rise to the top since his days at Udinese.
"Maybe we could kill him or knock him down or something," joked Montella. "I remember Sanchez really well from his time in Italy.
"He has improved a lot his style in his career and he's a really good player in terms of the transitions and finding spaces, and has a really good speed in attack."