Despite wrapping up their 20th championship with four games to spare last season and eventually finishing 11 points ahead of their nearest challengers, Manchester City, United were only third favourites in most bookmakers lists.
That situation remains the same, even after their impressive 4-1 win at Swansea on Saturday, with Chelsea and City tipped to scrap it out for the main prize instead.
Given Paul Scholes is the only departure so far and Wilfried Zaha has been added, it is a strange situation, and one the only explanation for is the exit of Sir Alex Ferguson and appointment of David Moyes.
Yet, according to Evra, it is not a new phenomenon.
"It is not just this season," he told MUTV. "It is every year.
"I have been here eight years now and every year people say we are going to finish fourth or fifth in the league. It is unbelievable."
Although there was an element of rustiness about United's play, especially early on, the eventual outcome at the Liberty Stadium was not the performance of a club whose standards have dramatically slipped.
Evra is not bothered about the wider message it has sent out to the league. But he does feel it will have reminded his own dressing room of their status.
"The way we are working we feel good," he said.