Opposite number Mick McCarthy experienced yet another defeat in the competition as he has not won a tie during his six seasons in charge at Portman Road.
It was 40 years ago that Ipswich won the cup but they never had a meaningful shot on the visitors’ goal throughout the 90 minutes of play on Saturday.
The only goal of the game came from Nathan Thomas in the 25th minute as a wonderful strike from 25 yards out flew into the right-hand corner of Ipswich goalkeeper Bartosz Bialkowski’s net.
The result sent the thousand-strong United fans home happy while the frustrated Ipswich faithful chanted: “What a load of rubbish” at the full-time whistle.
Wilder said: “I think we had some good chances just after half-time to take the game away from the opposition so we were a bit frustrated that we didn’t.
“Both teams made a few changes and, fortunately, our changes were just a touch better on the day than the opposition.
“It was a good goal... a cracking strike to win it.
“The consistency of the attitude by my team pleased me immensely and I have really enjoyed today. It wasn’t a free-flowing performance but it just shows what our players are all about. When they pull a shirt on, they want to win.”
The nearest the Suffolk side came to scoring was when Callum Connolly headed over the bar in the 66th minute following a cross from Bersant Celina, but Bialkowski was kept busy throughout.
Tractor Boys chief McCarthy said: “I thought we played well until the goal. I’m not unhappy with the performance, I’m unhappy with the result.
“We had an appeal for a penalty, which could have been given, but I’ve no idea what a penalty is now, having seen them all this week.
“But it did hit his hand and it could have been given and then he (Thomas) fits one round the top corner... that was the difference in the game. Our final pass and final cross wasn’t good but they are a good side and defended well and sat back and it was difficult for us to break them down.”
Asked about the crowd’s reaction at full-time, McCarthy added: “I can only do my best to try to get my team to win games and if we do I guess we get cheered and if we don’t I guess we get jeered.”
Ipswich Town: Bialkowski, Iorfa, Chambers, Knudsen, Kenlock, Connolly, Hyam (Waghorn 61), Sears, Bru, Celina, McGoldrick. Unused substitutes: Skuse, Garner, Crowe, McLoughlin, Webber, Drinan.
Sheffield United: Blackman, Carter-Vickers, Stearman, Wright, Baldock, Carruthers, Thomas (Slater 46), Basham, Lafferty, Sharp (Fleck 88), Lavery (Donaldson 72). Unused substitutes: Moore, Stevens, O’Connell, Norrington-Davies.
Referee: M Jones (Cheshire).