Highlights
Wednesday dominated throughout the game and, in the 21st minute, Gary Hooper saw a drilled 25-yard effort hit the post.
In the 64th minute, he did one better and notched his side's opening goal after reacting quickly to a parried save by Cardiff keeper David Marshall.
Wednesday doubled their lead in the 75th minute in bizarre circumstances after a mistake by Marshall allowed Hooper to steal the ball and cross towards the empty goal. Cardiff defender Peltier could only divert the ball into the net with Lucas Joao lurking.
Hooper added a third in stoppage time, chipping the keeper from inside the area after a neat flick-on from strike partner and substitute Atdhe Nuhiu.
Carvalhal said: "I said from the beginning that we were outsiders this season. We achieved this place because we have a fantastic group of players, they're acting like a team, we are one as a team.
"We did very well in this kind of game - the sort of game to decide things. The answer today was fantastic, it was a very good performance, we attacked very well, we defended well.
"We are the team that have a new coach, a new philosophy, we've changed a lot of things in the club.
"We feel strong at the moment, like at the beginning of the season. We saw that today. We saw the reaction when we lost the ball - we were like dogs.
"We have a lot of goals in our team but we have also equalled the record for clean sheets at the club, it's something we are happy with. We've found a balance.
"Getting to the play-offs is the work of a lot of people; the players, the chairman, the fans who turn out home and away."
Cardiff were the only club who could prevent the Owls from claiming a top-six berth before the start of play but they fell short in their quest.
Manager Russell Slade said: "It hurts. You're disappointed whenever you lose a football match.
"For half a game we were still in it but we're very disappointed with the second half and, in particular, the goals we conceded.
"It was frustrating we never kicked on. If you stay in the game the pressure would have mounted on them but we weren't able to apply that and we weren't a great enough threat in the second half.
"We tried whatever we could, bringing on bodies and we had three up front and three at the back by the end but you have to say we got beat by the better side.
"We need to finish on a positive note, we've been strong at home, we've made progress from where we were.
"Last year we finished in the top half and if we can finish seventh it's progress, just not quite enough."