Notably, with the match barely under way, Pablo Counago's strike from the edge of the area hit the post and rebounded into the path of Shefki Kuqi.
The Finnish striker's header found the back of the net, but the goal was disallowed although there was no evidence of off-side or anything approaching a foul.
Irritated but undeterred, Ipswich continued to surge forward, with some of the passing in the final third of the pitch worthy of the Premier League.
Tommy Miller hit the outside of the upright on 19 minutes, after referee Andre Marriner intelligently waved play on following a dreadful Wayne Brown foul.
After the Ipswich midfielder had missed the chance, Marriner handed Brown an inevitable booking.
Soon afterwards, brilliant work from Counago inside the area saw play swept out to the left, but Alan Quinn scuffed his shot wide.
Quinn produced a much better effort from further out later on, but just cleared the crossbar, and three minutes before the interval Kuqi should have forced a save from Boaz Myhill, but hit a weak shot wide.
Hull started better in the second half, but Ipswich's passion saw them surging forward again as they continued to make advances on Myhill's goal.
Counago missed from 10 yards after a great run and pass from Owen Garvan, Quinn squandered two further chances and only Andy Dawson's excellent tackle on Counago prevented another golden opportunity.
But in the 69th minute, Lee scored moments after replacing Quinn.
His initial touch, a header to Walters on the left, was played back to the substitute who nodded into the bottom corner of the goal.
Ipswich comfortably held out for the remaining 20 minutes, but the victory could not mask their disappointment at missing out on the play-offs.
Hull manager Phil Brown: "Watford are not the form team of the moment so we'll probably be favourites.
"It's a lottery now. We're in the semi-finals of a cup. But over the 46 games, the players have been superb.
"We're disappointed we are just in the play-offs. Today was a bridge too far." More Hull quotes
Ipswich manager Jim Magilton: "We're going to be bringing in better players.
"We're going to get rid of the players who are not going to take us forward.
"It's a building process and we're getting there. No one said it was going to happen overnight."
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