Jos Luhukay said the Owls were beaten by the better side as Middlesbrough emerged triumphant by the odd goal in three at Hillsborough.
Wednesday rallied late on as another Adam Reach stunner halved the deficit but Luhukay conceded that the best team won on the night.
He said: “There is no doubt that Middlesbrough were the better side this evening. We pulled one goal back late and might even have got an equaliser near the end from Barry’s corner.
“Although both their goals came from mistakes of our own, they were the better team and deserved the win.
“But I would have taken the point for sure because as we saw here recently against West Brom, you do not always get what you deserve in football.”
The Owls boss added: “This was always going to be a difficult game as Middlesbrough are a big, strong side at both ends of the pitch.
“They defend set pieces well and are strong on the counter. I thought we dealt with this okay and it was our mistakes that cost us the game.
“Now for me it is very important that we respond in the correct way at QPR on Tuesday.
“This is a big game for us and I want to see a better performance because successive defeats will see you slowly move down the table.”