A Sergio Aguero double and goals from Yaya Toure and Samir Nasri condemned David Moyes to defeat in his first Manchester derby, but the defender is keen not to lay the blame at the Scot's door.
"It is horrible to lose the derby game," Vidic told Sky Sports. "It hurts. Trust me, no one will want to remember this. "It doesn't matter whether we are losing or winning you will always go back to that question. Is the manager good? Are the players good?
"I am not looking at it that way at all. This is a club that has a history. This is a club that has players who have won so many titles and the players are all national team players. There is so much experience.
"This loss has hurt but the most important thing the new manager and the old manager said was that you have to bounce back and win the next game."
Vidic partnered Rio Ferdinand at the heart of defence for third match in a row, the first time they have enjoyed a similar run in the first team for nine years, and the Serbian has admitted the team struggled from the off.
"We cannot be sad and feel sorry for ourselves," he continued. "We cannot afford to do that. We have to stay true and improve certain things and then win.
"From the first minute they tried to be aggressive. They had more possession and we didn't really get in the game from the first minute. This is what we have to learn."