The Manchester United defender believes the league leaders will take full advantage of their two home fixtures before the New Year after they were held at the Liberty Stadium
Michu cancelled out the left-back's opening goal to hold Sir Alex Ferguson's team to a draw at the Liberty Stadium and allow Manchester City to close the gap at the top of the table to four points.
United face Newcastle at Old Trafford on Boxing Day before hosting West Brom and Evra feels optimistic about their chances of strengthening their grip on top spot on home turf.
"I felt that we deserved to win at Swansea and that is why I am really confident for the rest of the games we having coming up over Christmas," Evra told MUTV.
"We have to move on from the draw [on Sunday] and focus on our next game against Newcastle. It is important to win and it is important that we keep playing well.
"I think we need to talk about ourselves and not about another team [Newcastle]. We face Newcastle at home, let's make sure we get three points. After that it is West Brom and we must make sure we get three points then too.
"This is an important part of the season and it is an opportunity to get a lot of points. I'm not worried, I am really confident for the games coming up at Old Trafford."