Chelsea looked clear favourites for the title in the opening of weeks of the season.
Evra told manutd.com: "I respect every team in the league, but you have to remember Chelsea beat a couple of the teams who had just come into the league. But when they had their first big test against [ Manchester] City, they lost.
"The way things went at the beginning of the season didn't scare me. I know we made mistakes and dropped some points away from home, but I was not afraid that Chelsea kept winning five- and six-nil. It may sound strange but I was always confident. And we actually ended up with a better goal difference than them."