Gary Hooper scored twice for the hosts after a wonder strike from Fernando Forestieri gave them the lead. Gary Madine and David Wheater were on target for Bolton.
“I’m very happy about the victory because it wasn’t easy for us,” Carvalhal said.
“We followed the melody of the opponents in the first half but then we put different music on the pitch. In the second half we introduced a little rock!
“When you open the team, you take risks and both teams had chances. It was a very tough game and the important thing was the three points.
“I am happy with all the players and we are doing very well. We’re playing attacking football and our fans are very happy with the football we are playing.
“I know Gary Hooper very well and he’s doing well but I think he can do even better in the future.”
Bolton boss Neil Lennon said: “I thought we were excellent and I didn’t think we deserved to lose.
“In the second half we had two or three great chances to win the game. I thought Gary Madine was outstanding and I need more performances like that from him.
“We were playing against a team who’ve invested a lot and I was very encouraged by the performance.
“There’s a lot of speculation surrounding a lot of our players and it’s not an ideal situation but we have to raise money soon to keep the club going.
“I’ve not seen Mark Davies since Thursday and I don’t know if the deal (to Sheffield Wednesday) is done. I’d like to know one way or the other.
“Zak (Clough) was down at Bristol (City) on Sunday and again that’s not been concluded either so he’s back in the squad.”
Sheff Wed: Wildsmith, Hunt, Loovens, Sasso, Pudil, Wallace,Lee, Bannan, Forestieri, Nuhiu, Hooper.
Subs: Palmer, Semedo,
Helan, Lucas Joao, Lopez, Sougou, Price.
Bolton: Amos, Holding, Dervite, Wheater, Moxey, Vela, Trotter, Feeney, Wellington Silva, Pratley, Madine.
Subs: Spearing, Clough, Rachubka, Danns, Casado, Ameobi, Woolery.
Referee: Simon Hooper (Wiltshire)