The Red Devils finished the 2011-12 campaign without silverware following their exit from the cup competitions and losing their grip on the Premier League title to Manchester City on goal difference.
Following last year's disappointment, United were crowned English champions courtesy of a 3-0 win over Aston Villa last month with five games left to play.
"We enjoyed it the best we possibly could," Valencia told the club's official website. "It's a fact now and you can't take that away from us. We've won the title after a very long season and we managed to achieve our aim.
"Last year was terrible – a trophyless season. We can't go two seasons without bringing home some kind of silverware so the aim was to win something and winning the title fits the bill perfectly."