Carlos Carvalhal refused to point the finger of blame for his side's FA Cup crash at the hands of Middlesbrough at the Riverside.
A howler from the young keeper gifted the home side the second goal, while they were down to ten men, and effectively killedthe game off and booked Aitor Karanka's side a place in the fourth round.
Wednesday had fielded a strong line-up against the Premier League opponents but they struggled to gain a foothold on the game.
Grant Leadbitter put Boro in front with a 25 yard free kick before Danny Ayala was red-carded for a challenge on Fernando Forestieri.
However, Wednesday never grasped the numerical advantage and Middlesbrough doubled their lead when Alvaro Negredo charged down Wildsmith and the keeper's attempted clearance went into the net.
That signaled the end for Wednesday and a flattering gloss was put on the scoreline by Marten de Roon in injury time.
Carvalhal, though, despite the fact that the second goal proved so crucial, played down the error from Wildsmith.
"All of us have responsibilities. I never put responsibility on one player because we lose one game, we lose together," he said afterwards.
"I think we didn't give the goalkeeper much to do before this period, Middlesbrough didn't give Joe much to do either. We balanced completely.
"It was very difficult to go inside, it was very difficult for them to go inside because of our defensive organisation. They scored with a free kick where we had everything under control and another goal, that's part of the game and the third, ok, we were trying everything, we had five attackers, we broke the game, we had nothing to lose. I don't have much else to say."