Kenny Jackett was frustrated after Millwall blew the chance to ease their relegation worries ahead of their Wembley day out.
The Lions, who face Wigan in the FA Cup semi-final on Saturday, were leading Sheffield Wednesday after Jimmy Abdou fired them ahead within just 63 seconds.
But Miguel Llera pulled one back before the interval and Chris Maguire sealed a 2-1 win in stoppage time as the Owls, who kicked off three points above the drop zone, leapfrogged their hosts in the table.
"For large parts we were in control, we've let Sheffield Wednesday off the hook in the end," said Jackett. "We got an early goal, at home, and so we should have gone on to win that game. But I didn't feel we were looking at Saturday. Their keeper was the busier.
"I know 52 points won't be enough and four of our six games are at home. In this competition we still have work to do. A points target is a tough one to call. We realistically should beat our total of last year, 59, and I wouldn't want to think the FA Cup had interfered with that."
Millwall are unlikely to find Wigan as charitable as Wednesday, who conceded the opener with the first attack of the match. Chris Taylor was allowed to cut in from the left wing, charge into the penalty area unchallenged and deliver a low cross for the unmarked Abdou to bundle home at the far post.
But five minutes before half-time the Owls drew level through Llera, who curled a 25-yard free-kick around the wall. Millwall keeper David Forde appeared to have the shot covered but the ball bounced in front of him, over his hands and into the net.
Both sides had chances to win it but it fell to Maguire to hook in a corner deep into injury time to secure a valuable three points.
"We weren't going to let them go into the semi-final in relaxed mode," admitted manager Dave Jones. "It was a good finish for the winner. It was the best time to score - with 30 seconds left.
"Everybody's done their job, certainly in the second half. In the first half I was disappointed with the way we started but our first goal settled us down. It could have gone either way. We both had chances."