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."
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."
