Pogba was widely viewed as the man who would be the star of France's bid for glory on home soil, but has largely failed to convince ahead of Sunday's quarter-final with Iceland at the Stade de France.
Following a listless showing in the tournament opener against Romania, he was dropped to the bench alongside Atletico Madrid star Antoine Griezmann and featured as a second-half substitute to help Didier Deschamps' men make it two wins from two versus Albania.
Griezmann definitively made his mark on the tournament with a brace as France beat the Republic of Ireland in the last 16, although they fell behind after Pogba conceded a second-minute penalty.
Evra also played alongside Pogba during the latter's formative years at Manchester United – a club he has been linked with a return to – and urged calm while facing a string of questions over his star colleague at France's Clairefontaine training base on Thursday.
"Everybody thinks I am Paul's dad," he joked.
"It's not just Paul, it's Griezmann – leave them alone a little bit. It's not [about] Griezmann or Pogba – it's the French team.
"Paul wants to do well, he wants to succeed. In football you can't always succeed.
"He is very good and very happy – don't worry. He will respond when we need him like Griezmann did in the previous match."
The 35-year-old sounded a similar tone in defence of Olivier Giroud – the Arsenal striker who has regularly found himself bearing the brunt of criticism at international level.
"When I talk about Olivier Ground and the fans and journalists who criticise him; if you criticise Giroud then you are criticising the French team," Evra said.
"It was Griezmann who scored the goals, but [Giroud] did the flick-on for the second goal against Ireland.
"You have to leave people alone. We have confidence in everyone. If Giroud is here it is because we need him and the trainer has confidence in him."
Above all, it is the strength of the collective under Deschamps that Evra thinks will define France's campaign.
"I can speak until tomorrow, then we must show an example on the pitch," he added. "Everybody has to think that there are a lot of players who would love to be in our place.
"Every day the players take this into consideration.
"There are no worries, everybody has confidence. One guy is not here to sell a dream, everyone has to do this together.
"If somebody wants to be a star, we talk to them and put them back in their place. The star is the team, not the individual."