Iceland came from behind to record a stunning 2-1 win in Nice, a result that prompted the departure of England boss Roy Hodgson.
Former Manchester United left-back Evra expected England to prevail, but is adamant the host nation will not repeat their mistakes in the concluding last-eight match at the Stade de France.
"I said it's logical that England would win, but it's always 50-50," said the 35-year-old Juventus defender.
"There are a lot of people who have underestimated the so-called inferior nations. This tournament is difficult.
"At the end of our match [against the Republic of Ireland in the last 16] there were a lot of English journalists who spoke about playing France. You know in football anything can happen. Let's see what happens now.
"In football you have to never underestimate your opponent. What worries me a little bit is people say the English did not respect Iceland
"We have to tell them 'bravo'. They have done everything for their people. They have great fans. It's going to be a complicated match.
"I played in England against [Gylfi] Sigurdsson and he is a great player.. They are not just players who play with throw-ins. They know how to play triangles.
"I respect this team and there are options not to fall into the trap [that England did]."
France struggled to impose themselves during the opening stages of last-gasp group victories over Romania and Albania at Euro 2016, while they fell behind to an early Robbie Brady penalty before seeing off Ireland in Lyon.
Evra – who confirmed he is fit to face Iceland despite suffering a finger injury during training on Wednesday – acknowledged the need to address these sluggish starts, sounding a further warning against a complacent approach versus Iceland.
"It's true, the beginning of our matches are not good," he said. "It's one of our problems – we are reacting.
"We have spoken among ourselves that this team need to have their backs to the wall. It is a problem.
"Against Iceland we need to attack this match and not wait until the second half for some acceleration.
"We have to wake up before the matches."