Evra says Moyes has the full backing of his players as they fight to bridge an 11-point gap between themselves and fourth-placed Liverpool by season's end.
He told RMC: "There was a big change, it must be digested - nobody likes change. The team played for over 28 years with Alex Ferguson.
"It is behind the new manager, we will do everything to qualify for the next Champions League."
Of his own future, Evra added: "I love Manchester. When my love will be broken with Manchester, I will study the possibilities."
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