The Owls signed off the 2013/14 Championship campaign with a 2-1 defeat to Ipswich at Portman Road on Saturday.
Tommy Smith set the ball rolling for the home side, finishing on the rebound before half time but Kieran Lee equalised with his maiden goal for the Owls after the break.
But the Tractor Boys went on to claim the win with Paul Green on target with a glancing header from a free kick, as Mick McCarthy’s men finish just three points outside of the play-offs.
Ipswich saw their hopes of a top-six finish come to an end last week after defeat at Burnley and almost fell behind to an early goal.
The ball fell kindly to Michail Antonio in the area on the left but the winger blazed high over the crossbar.
The Tractor Boys, though, responded with a positive move of their own as the lively Jonny Williams burst into the area at pace, only to be thwarted by a crunching Glenn Loovens challenge.
But Wednesday were powerless to prevent the opening goal of the half in the 36th minute after a spell of heavy pressure from the hosts.
Daryl Murphy sent a curling effort towards goal that Damian Martinez did well to keep out with a firm hand but Smith mopped up the rebound from close range to give Ipswich the advantage.
Buoyed by the breakthrough, Ipswich came within the width of the upright from adding a swift second goal to their tally.
Murphy went on a mazy run and after cutting inside the area from the right, blasted against the inside of the post and Wednesday were able to clear the danger.
Moments before the interval, ex-Ipswich man Caolan Lavery brought a fine save from Dean Gerken and from the resulting corner, Antonio almost found a route to goal but Gerken made another key reaction save to keep his side in front heading down the tunnel.
Dangerman Murphy planted a firm header just over the top after the restart as Ipswich aimed to strengthen their hold on the game.
But the Tractor Boys were made to pay for that miss as the Owls levelled with the next attack.
Chris Maguire delivered a low centre from the left and as Lavery miscued in the middle, Lee was on the spot to sweep home into the bottom corner.
In the moments that followed, Wednesday largely had the upper hand but Ipswich were able to ride that brief storm and regain their lead from a set piece.
Substitute Stephen Hunt delivered from the right and Green glanced into the far corner out of Martinez’ reach.
Still, there were chances at both ends and the returning Jacques Maghoma dragged just wide of the near post for Wednesday but Ipswich held on to record their 12th home win of the campaign.
Ipswich: Gerken, Cresswell, Chambers, Smith (Taylor 64), Berra, Murphy, Wordsworth, Green, Richardson, Williams (Hunt 64), Nouble (Marriott 86)
Owls: Martinez, Lee, Loovens, Onyewu, Mattock (Helan 75), Antonio, Coke (Maghoma 81), Lavery, Maguire, Hutchinson, Nuhiu (Best 61)