Forestieri joined Wednesday from Watford in the summer transfer window, and his capture has been one which has particularly pleased the Portuguese boss.
Carvalhal says that Forestieri was one of his top targets, and he was impressed by his debut performance in his side's 3-1 defeat to Burnley at the weekend.
"I said before the match that our fans would love him, and he proved that," Carvalhal said. "He didn't play a long time last season, he played a few matches, and he will do better game by game. He is not 100% yet, but we think he can do much better.
"The players like to play with him, not just the strikers but the wingers too, because all the time they have a solution. He is a player who is very important to us and I am very happy to bring him here.
"I pushed a lot for us to sign him. You don't imagine how much energy I gave towards us to sign him!"
Forestieri joins Wednesday soon after helping Watford gain promotion to the Premier League, and his quality is undoubted.
The mercurial attacking midfielder is a natural in possession and his creativity should add a further threat to Wednesday's already impressive squad.
The Owls have the more powerful Atdhe Nuhiu and Lucas Joao who can partner Forestieri up-front, meaning he should compliment them nicely.
It was Nuhiu who partnered Forestieri on his debut and the duo showed signs of promise, which they will be hoping to build on when Wednesday take on Bolton Wanderers tonight.