The Blades laboured to a 2-1 Roses win over Rovers at Bramall Lane and resembled a side who had made ten changes from the weekend, with Wilder giving the night off to several of his leading lights ahead of the league trip to Chelsea.
Progression to round three was the saving grace, but Wilder admitted to mixed feelings on the night.
Wilder said: “I take the blame for possibly a disjointed performance.
“When you do make that many chances and play so many shapes as we have done, it is not really the players, but me rather in terms of how I have gone about it.
“But you get some games where you do not have a rhythm about you.
“It was similar to the Barnet (FA Cup) game last year where you make that many changes that you do not get into a rhythm. But we had to make the changes as everyone realises that the bigger issue is Chelsea on Saturday.”
The evening saw Ravel Morrison, Mo Besic and Ben Osborn make their full competitive debuts for the Blades, while £9.5million arrival Lys Mousset was handed his bow from the bench.
The input of former Manchester United and West Ham midfielder Morrison in the middle of the park particularly augured well in the view of Wilder.
The Blades chief added: “We changed about four or five times and Ravel was nice and bright and good in possession. He is a talented boy, although he gets himself frustrated a little bit now and again and maybe frustrates other people.
“But you can see he is comfortable in possession and Mousset coming on was a real bonus. And I knew I would get performances from the likes of Jags (Phil Jagielka), Richard Stearman and Billy Sharp.”
Four Yorkshire-based players have been named in Northern Ireland’s squad for the forthcoming Euro 2020 home double-header against Luxembourg and Germany in Belfast.
Leeds United’s Stuart Dallas is in the squad alongside Middlesbrough duo Paddy McNair and George Saville and Hull City forward Josh Magennis.
Ex-Leeds keeper Bailey Peacock-Farrell is also in the party alongside former Sheffield United forward Conor Washington.