United exited the Champions League at the group stage last season before being dumped out of the Europa League and then losing their Premier League title on the final day to rivals Manchester City.
But with Sir Alex Ferguson demanding a fast start from his players, Valencia is eyeing success in Europe as well as the domestic league.
Valencia, quoted in the Daily Star, said: "All the players are feeling good about the new season and there is a great team spirit amongst everyone.
"I love being part of this team. I have some good friends here and I laugh a lot with guys like (Patrice) Evra, Nani, Anderson, Bebe and Chicharito.
"Everybody in the group has a laugh together but when we have to work, we take things seriously.
"I'd love us to win all the competitions we play in, particularly the Premier League and Champions League."
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.