United lifted the Carling Cup on Sunday as they beat Tottenham on penalties after a goalless 120 minutes of action to add to the Fifa Club World Cup they won in December.
With the club odds-on to retain their Premier League crown, and favourites to progress into the latter stages of both the UEFA Champions League and FA Cup, United could sweep all before them.
But Evra was adamant that, although such a feat was achievable, it was something for the press to talk about rather than the squad.
"Five titles this season? We have the right team to do it," he told L'Equipe.
"But we can't put that in our minds. We can make it but we will need to be lucky, as today.
"The press talks a lot more about five trophies than us in the changing room."
TiredThe usually assured French international was given a torrid time in the Carling Cup final by Spurs winger Aaron Lennon and he admits that it was not his best game.
"I don't want to look for excuses, but we had the Inter match in the legs," he added.
"I am just back from injury and it was my fifth match in ten days. Lennon played a great match, but the trophy is in Manchester, that is the only important thing."
The League Cup success was his sixth major honour since joining the club in 2006 and the former Monaco man admits he is just waiting for one more medal to complete his collection.
"It is impressive when my friends told me about my trophies," he revealed.
"I tell myself some players will never win that in a whole career. I just miss the FA Cup. I hope it will be this year. That left me wanting more."