The Red Devils reclaimed the trophy from Chelsea last month following an impressive campaign that ultimately saw them finish nine points clear of their nearest rivals.
However, United's triumph was built on an excellent home record with their form on the road far less dominant.
Sir Alex Ferguson's men won just five away games in the Premier League and French left-back Evra is determined to do much better in future.
The problem we had was our away form. I just dont understand why we didn’t win more games away from Old Trafford, he said in the Daily Mirror.
"We just didn't play the same way we did at Old Trafford. It was our home form that won us the league.
"Just imagine if we can start winning away - we could win the league by 15 points.
"We have to resolve the problem with our away form. As I said, I don't know why it happened this season but next year we will make sure things change."
Evra was delighted to help United overhaul Liverpool as England's most successful club but is now looking for title number 20.
"Every time we went to a restaurant or walked down a street this season the fans wanted to talk about it," he explained.
"But we are not finished yet. This is just the beginning. I know Manchester United can win more titles and we just have to keep doing that.
"What has happened is a great achievement but we have the quality players to win more than the 19 titles."
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