Jordan Rhodes' first-half header was the difference between the teams at the KCOM Stadium but Hull thought they had equalised in added time when Abel Hernandez's effort landed in the back of the net.
But after some discussion between referee Scott Duncan and the linesman, the goal was ruled out.
Speaking about the incident, Adkins said: "I've just watched it back on the replay now. We score a goal, the referee indicates a goal and points to the centre circle.
"The linesman runs towards the halfway line as they normally do when indicating a goal and obviously we're celebrating then.
"And one of the players has asked the referee to go and speak to the linesman. They've had a conversation and disallowed the goal for offside.
"They both actually gave a goal then they've come up with the decision that it's not a goal.
"It's very, very close. It doesn't matter whether I agree or disagree - it's given as offside and we lose the game.
"For me there was an opportunity today."
Wednesday started the game brightly and only a smart save from Allan McGregor prevented Rhodes from heading them in front in the fifth minute when Adam Reach picked him out in the box.
After Max Clark's long-range effort had drawn a good save from Joe Wildsmith, the Owls broke the deadlock when Rhodes nodded in Jack Hunt's pin-point cross.
The hosts pushed for an leveller in the second period, with Hernandez going close on a couple of occasions but Wednesday managed to keep them at bay until stoppage time.
Shortly after the fourth official had signalled there would be eight minutes added on, Hull had the ball in the back of the net, but after a short delay as he conferred with the referee, the linesman raised his flag and ruled the goal out.
The Owls' victory moves them up to 50 points and all-but secures their Championship safety.
Boss Jos Luhukay praised the character of his side.
He said: "When we saw the last games from Hull, four and five goals scored while we lost the last two games, (we knew it would be) a very difficult game for us.
"The mentality and the character in my team is fantastic. Last Tuesday we lost three players for today - Atdhe Nuhiu, Lucas Joao and Daniel Pudil - but the players who came in did a very good job.
"As a team we are strong and we stay together. On Tuesday we lost as a team and today we won as a team and that makes me very happy.
"I think it was a good game. Of course for us, the first half was better than the second."