The U’s put their timid midweek defeat at Queens Park Rangers behind them with an encouraging first half against the Owls, but then saw their hard work undone in the second period.
Greg Leigh gave United the lead, only for Josh Windass to level in an entertaining first half.
Strikes from Jamal Lowe and Djeidi Gassama put the Owls in control though after the restart, and the U’s never looked like clawing themselves back into the match.
United head coach Buckingham said: “We asked for a response from Wednesday in terms of being a lot more creative and attack-minded in the final third, and we certainly got that in the first half.
“As corny as the saying is, goals change games and we had some big moments to extend the lead.
“I thought we were deserved of being 1-0 up and we had two or three big moments afterwards to make it two.
“I’m happy with the reaction, certainly in the first half, and then I’m just disappointed with how the second half has played out.”
The Windass goal came from a corner, while a ricochet in the box landed kindly at the feet of Lowe for the Owls second.
Buckingham said: “You put things in context when you can. We are still one of the strongest sides from defending corners in the league.
“You don’t want to concede any, but if you’re using that as a measuring yard, it’s always a good starting point.
“It was a scrappy one that put them back in the game and gives them a bit of belief.
“And the second one, we don’t quite get those falling for us at the moment, but that’s the way it is here at the minute.
“We’re in a bit of a run with how things are going, and it takes the stuffing out of you a little bit to go 2-1 down.”
Buckingham added: “We’ve all played the game or been in the game long enough to know what we’re trying to do, and what’s good and what isn’t, whether it’s performance or set-up.
“As long as we stick to that, we’ve shown the success of that together as a playing group, a staff group, a club, and as a fan group.
“We’ve shown what that brings and that’s always been something we’ve been able to fall back on, so it’s making sure in these moments, we recognise they are challenging moments, but we will find ways to continue challenging ourselves at this level, and also we put things in place to get us results.”