Irvine admitted his disappointment but refused to be too downhearted with the final score.
"It definitely feels like two points lost, but even if we had won I'd have still said we need two wins to feel comfortable," Irvine said.
"It was a performance that deserved three points but we move on. We could have done with the points but it's gone now and we need to take the same level of performance into the coming games. If we do, we'll win.
"We know it was a bad goal to concede but you can't dwell on it and make it cost you further. It has today - we've not got what we deserved - but we must respond to the set-back in the right way."
Coventry were second best in the first half and had keeper Keiren Westwood to thank in the fifth minute after he pushed Darren Potter's low drive wide.
The Owls brought the best out of Westwood again when Eddie Nolan burst past Marcus Hall and shot low, but the Republic of Ireland international palmed the ball away.
In response to Wednesday's dominance, Chris Coleman made three half-time changes - and got the reaction he needed.
A 53rd minute Clingan corner found James McPake whose header went just over the crossbar and a minute later sub Clinton Morrison finished a Freddie Sears pass - only for it to be flagged offside.
But as Coventry pushed forward, they left holes at the back and Westwood was the hero again when he pushed a 60th minute Leon Clarke header onto the post.
Then the Owls took the lead through Varney. The forward picked up the ball on the left wing and drifted inside the box, beating David Bell twice, before firing home from a tight angle for his ninth of the campaign.
The goal could have moved the visitors away from the relegation mix, but when Clingan launched a long ball in the 78th minute, Wood was on the 18-yard box to head over the advancing Lee Grant to score.
Coleman said: "We made three tactical changes and it was a bit better second half. But we have to play from the first minute, not the 45th.
"We played here a couple of weeks ago against Cardiff and, had we won, we would have been in the top six. But, instead, we lost late on and it was through no fault of our own, it was down to a decision from an official.
"That's taken its toll on us but we've spoken about the end to last season when we didn't win for seven or eight games and we can't have a repeat of that."