Carlos Carvalhal rued a second successive play-off heartbreak and insisted the Owls must dust themselves down and return stronger for another assault on promotion.
Huddersfield emerged victors from the Championship semi final second leg, winning 4-3 on penalties following a 1-1 draw after extra time.
The head coach said: “We win together, we lose together and first of all, congratulations to Huddersfield.
“We are devastated but we must keep our focus as a club and continue the progress we have made over the last two years.
“We were in control of the game tonight after taking the lead but we missed one position in the pressing and made a mistake we do not normally make.
“But this is football – we had chances, they had chances and we go to penalties.
“This is the lottery of football and unfortunately there will be misses.
“But there is no blame, no one says a bad word to Sam or Fernando because it is Sheffield Wednesday who lose, not individuals.”
He added: “Overall I am very proud of my players for achieving the play-offs for two years because this is not an easy thing to do.
“This competition is hard. There are positives over the season but, of course, tonight is the big negative and I will not sleep before coming back in the morning.
“The club is moving forward, it is a better club and I must say thank you to the fans for their support tonight and we are so disappointed we could not win the game for them.”