United have struggled under their new boss this season, slipping 15 points behind Premier League leaders Chelsea and exiting both domestic cup competitions.
In addition, United were beaten 2-0 at Olympiacos on Tuesday in the first leg of a UEFA Champions League last 16 tie, but Evra insists Moyes retains the full backing of the squad.
"There was a big change, nobody likes change," the defender told French radio station RMC Sport, acknowleding the impact made by Ferguson during his lengthy tenure at Old Trafford.
"We are behind the new manager; we will do everything to qualify for the next Champions League, (and) my love for the club will not change."
"I love Manchester," he added. "When my love is broken with Manchester, I will study the possibilities.
"Everyone respects me, I feel at home here. It's beautiful.
"I have very good relations with the new coach."
