United conceded goals just before and just after half-time which killed the game for the Reds.
“To lose a derby game is horrible,” Vidic told Sky Sports. “It's more difficult when you lose the game after this kind of performance.
“We were 4-0 down and it was really tough. We were never close to winning the game or even getting a draw. It's disappointing but we have to come back. We're down now but from tomorrow we'll try to be positive and win the next game and move on."
City were the stronger starters in the match and took a foothold in the contest when Sergio Aguero gave the home side a 16th minute lead. United didn’t dictate play until the scoreline stretched beyond the Reds’ reach.
“From the first minute they tried to be aggressive,” added Vidic. “I'd say they had more possession in the first 20 minutes and we lost a goal. We didn't get in the game from the first minute. Obviously this is what you have to learn and now, the next game, we try to win. That’s the most important thing and we can't afford to look back.”
More: The Match: Reds overcome