The win was Spurs' first at Old Trafford in 23 years, and came after being 2-0 up at the break courtesy of goals from Jan Vertonghen and Gareth Bale, with Evra bemoaning the Red Devils' performance in the opening period.
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United rallied in the second half, with Nani and Shinji Kagawa netting, but were left with too much to do as Clint Dempsey hit a third with Andre Villas-Boas' side claiming the points in a scintillating encounter.
"The result is what happens when you only play for 45 minutes," Evra told reporters.
"The game is 90 minutes long and we deserved to lose because we only played for 45. To concede three goals at Old Trafford is not good enough.
"The problem is in our heads. It looked like we stayed in the hotel. The first 45 minutes had no speed, no focus, we didn't win a lot of challenges and we conceded some silly goals.
"Maybe I am hard with myself and the team but we only showed the United face in the second half. This is not enough if we want to win the title."