"We have to accept it has not been a great start," Vidic said. "We have not been getting the performances we would have liked and we also have to be realistic enough to accept we have made some mistakes.
"This team has a lot of potential and we are working really well ... I am really positive."
City manager Manuel Pellegrini also badly needs a victory after his side's crushing loss to Bayern Munich just days after defeat at Aston Villa.
Like Moyes, former Malaga manager Pellegrini has found it hard going since taking over and, ahead of Saturday's clash with Everton, City defender Micah Richards admitted they have to respond immediately.
City and United are already five and eight points respectively behind leaders Arsenal, who head to West Brom on Sunday with confidence sky high after a 2-0 Champions League win over Napoli.
Arsene Wenger's side have won five successive EPL matches to open up a two-point lead at the top.
Second placed Liverpool will expect to keep the pressure on Arsenal when they host struggling Crystal Palace.
- AAP