Salah - on loan from Chelsea - scored a brace as Fiorentina won the semi-final first leg over the Serie A leaders at Juventus Stadium.
Montella was proud of his team as a whole, but saved particular praise for Salah - who has scored six goals in his past six games.
"Salah is on fire at the moment," he told RAI.
"But the team as a whole has been playing consistently well since November and that makes a difference."
Salah opened the scoring in the 11th minute, taking a pass inside his own half before accelerating away and finishing past Marco Storari.
The hosts were level just 13 minutes later as Fernando Llorente headed in a cross from Simone Pepe.
But Salah's smart finish in the 56th minute proved to be the winner for Fiorentina.
Montella said his team, unbeaten in 13 matches in all competitions, were playing with a "swagger".
"I was worried about our opponents today and now I expect a really tough return leg. I feared we might ease up a little after our recent excellent results," he said.
"Instead we were brave and played with a swagger, especially at the start of the second half - that's when we won it. We showed we're a solid, mature side."
