Despite drawing 1-1 at the Emirates Stadium, Wilder was critical of his team’s performance with the ball before John Fleck scored a late equaliser.
Although he acknowledged the progress United have made since being promoted last term - they are seventh in the table and challenging for a place in next season’s Europa League - Wilder predicted Pep Guardiola’s side will not prove as forgiving as Arsenal if his squad fail to work smarter during Tuesday’s encounter.
“They have got some outstanding players, City,” the United manager said. “We had to work hard on the sideline at Arsenal, we had to change shape many times.
“We can’t give the ball away cheaply, like we did at Arsenal.
“If we have any designs to take something from the game, then we can’t do that again. No way.”
United were beaten in controversial circumstances when they travelled to the Etihad three weeks ago; Lys Mousset having a ‘goal’ ruled out by VAR before the referee impeded Fleck, allowing Sergio Aguero to claim the first of two City goals.
Wilder, who insists he is making headway in the transfer market ahead of this month’s deadline, wants to recruit two centre-halves to provide cover and competition for Chris Basham and Jack O’Connell.
Luke Freeman, a summer signing from Queens Park Rangers, was not named among United’s substitutes in north London, prompting speculation he could be allowed to depart.
Some reports have claimed Wilder will only sanction Freeman’s exit if a suitable replacement is found but The Star understands coaching staff believe the 27-year-old has fallen victim to the evolution of United’s tactical model, rather than any weaknesses on his part.
Wilder tempered his critique of their display at Arsenal by noting: “There was apprehension coming into the division. We haven’t got a lot of experience, or we didn’t.
“But we have a group that challenges each other. We aren’t a newly promoted side that had been unbelievably backed financially.
“The key for us now, is to turn that story into a fantastic one by keeping the hammer down right until the end of the season.”