Salah - on loan from Premier League outfit Chelsea - scored twice to help Fiorentina to a 2-1 victory over Juventus in the opening leg of their tie at Juventus Stadium.
The Egypt international produced another scintillating performance on the road as he took his tally to five goals in four games, having opened the scoring in the 11th minute via a stunning solo effort that saw him collect the ball in his own half and shake off three defenders before firing into the roof of the net.
Fernando Llorente equalised 13 minutes later, only for Salah to restore Fiorentina's lead 11 minutes into the second half.
Allegri conceded the better team won on Thursday but the Italian boss has not given up hope of upstaging Fiorentina in the return leg on April 7.
"Both teams played well in the first half, even though we conceded by allowing a guy to run 70 metres with the ball," Allegri told reporters.
"We should have been more alert. After the difficult 10 minutes we endured at the start of the second half, we started playing again, but Fiorentina were smarter than us and deserved to win.
"We've got the return leg and we'll give it a good go to reach the final, knowing it won't be an easy task. Fiorentina are a fine team in a rich vein of form."
Allegri added: "This result needs to make us sit up and take notice ahead of our next games in Serie A, which still isn't over.
"Now we'll prepare for an important and difficult encounter on Monday against Sassuolo."
