Jimmy Abdou had given the hosts the lead after just 63 seconds at The Den, but Miguel Llera pulled one back before the interval and Chris Maguire sealed victory for the Owls in stoppage time.
Jackett insists Millwall performed well and claims his charges were not distracted by this weekend's FA Cup semi-final against Wigan at Wembley.
"For large parts we were in control, we've let Sheffield Wednesday off the hook in the end," said the Lions boss.
"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."