The Red Devils defeated Chelsea in a penalty shootout in Moscow to claim their third success in the European competition, but Evra has admitted that the Scot was straight onto the players about repeating the triumph in the following campaign.
Evra told UEFA's Champions League Magazine: "[Ferguson said] 'Congratulations, but anyone who doesn't want to win the Champions League again next year, I will rip up his contract!' I thought to myself, We've just won the Champions League, he congratulates us for two seconds.
"Manchester United is a club with a winning culture. When you win a game it's not fantastic, when you win the league it's not fantastic, when you win the Champions League it's not fantastic, it's normal.
"That's the culture Sir Alex Ferguson imposed on Manchester United. For him, we were there to work and to win. That was the DNA of Manchester United."
Evra left United in the summer to join Juventus after an eight-year spell at Old Trafford.