The French left back scored in a 2-1 win over the Gunners at Old Trafford but feels despite also beating Chelsea last weekend, his side has to be more clinical in front of goal.
Evra scored the second goal in United's 2-1 win over Arsene Wenger's side, and with Chelsea and Manchester City drawing at Swansea and West Ham, respectively, Sir Alex Ferguson's team now leads the table by one point. Despite the club picking up maximum points from games against two of its closest rivals, Evra says there is room for improvement after his side wasted numerous chances on Saturday.
"We're a little bit disappointed we didn't keep a clean sheet, but in the end it was an important win, and that's what everyone was looking for before the game. It's been a terrific week for us," the French international told the club's official website. "The expectations are very high here and we should have scored more goals - we felt like we had lost the game in the dressing room afterwards."
Despite only winning by one goal in the end, Evra suggested it is important for his teammates to remember the caliber of opposition they defeated.
"If we had taken every chance we created it would have been a different game, but to only finish 2-1 is a bit disappointing," Evra said. "When [your expectations] are so high you can sometimes forget that you've beaten a team like Arsenal. It's a big game we have won."
The 31-year-old insists United can now look to reclaim the title it lost to Manchester City if it continues its form against the league's strongest sides.
"We've won at Liverpool, at Chelsea and now we have beaten Arsenal. Last season we didn't do that, and that's why as a team we know we have the potential and the quality to win the league."
Evra's second goal of the season gave United a two-goal cushion - one they needed considering Santi Cazorla's late consolation for Arsenal - but the left back insists points are his only concern.
"Accidents can happen, and it's happened twice now this season!" Evra said of his goal. "I'm really happy to score again but the most important thing is the three points."