Saturday's 2-0 home victory over West Brom provided United with only their fourth Premier League clean sheet of the season, compared with 10 at the same stage in 2011/12.
They have also conceded 28 goals already in this campaign after only letting in 33 throughout last term.
Left-back Evra said: "Maybe it sounds bizarre but I feel we were weaker defensively last year even if this season we have conceded more goals.
"I know sometimes it is about concentration and we can do much better but it does seems the opponent scores every time they shoot. I am not worried about the goals.
"The confidence of keeping a clean sheet is good. I am a defender. I don't like to concede goals.
"But I am more bothered about winning games and I know when we have a big game the defence will be strong."