He revealed how United went back-to-basics to get back on their feet after the embarrassing show against Manchester City.
The centre-back, 30, said: "It was important to show the 6-1 didn't affect the players and I think we showed that at Everton.
"It was important to defend like a team and get back to playing as a team. In the last 20 minutes against City we didn't do that.
"That's why we were disappointed. But since then we've come back to the way we used to play. When you lose a derby, especially by that scoreline, it is difficult to take — but we have shown character."
Vidic said United's players were not allowed to dwell on the humiliation handed out by City when they returned to their training base.
He said: "Hopefully we can prove that the derby was just one bad day.
"We haven't come to training with our heads down. We have worked harder because we want to play better. This is the right mentality to have.
"When you lose games you can always look at the things you did wrong and what you can improve.
"Losing that game was difficult but it's important to look forward. Even when you win you can't spend time celebrating, you have to focus on the next game."