Les Bleus dominated possession, and made twice as many passes as their opponents in the Donbass Arena.
However, they were unable to find a second goal once Samir Nasri had levelled Joleon Lescott's point-blank header before half-time as England defended doggedly in Donetsk.
"We are frustrated because I think we played much better," said Manchester United star Evra. "At times it was like there were 15 bodies in front of us. It was really difficult to find space.
"People laugh but they played the way that Chelsea played against Barcelona.
"Maybe the fans want England to play more football but if they win the tournament like that, they will be happy."
Nasri was crowned man-of-the-match by UEFA for an excellent overall display.
The Manchester City midfielder was barracked by England's fans, presumably for the manner of his big-money move from Arsenal last summer.
It triggered a reaction from Nasri after his goal, where he put a finger to his lips in a silencing gesture, although manager Laurent Blanc was unaware of why.
"That's between him and his detractors," said the France coach. "That is something personal.
"There are individual and personal reactions. These are things we don't always expect.
"I think Samir was happy to score a goal and play a good game. You'd have to ask him who he was directing that (gesture) to."
Meanwhile, Nasri revealed he deceived City team-mate Joe Hart in order to score his goal.
"When Franck Ribery gave me the ball, the England defence was really low (sitting back)," said Nasri.
"I decided to take a shot but Joe Hart knows me from Manchester City and knows that in that situation, I normally open my foot.
"This time I closed it a little bit so I am happy with how it worked out."
Although Nasri was disappointed France only collected a point, he accepts it is already a vast improvement on the debacle that unfolded in South Africa two years ago.
Laurent Blanc's men have taken their unbeaten run to 22 games and are in good heart ahead of a meeting with co-hosts Ukraine in Donetsk on Friday.
"We are making a lot of progress," he said. "We have come from nothing in 2010, when we made a lot of mistakes.
"Today we are more mature. We can do something with this group."
Nasri played down the massive ice-pack he had strapped to his knee, insisting it was "nothing serious".
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