Juan Mata said Manchester United know they have to respond to the disappointment of finishing seventh by winning the Premier League next season.
United have not gone two years without a league title since a three-year drought between 2004 and 2006, which is they only time in the Premier League era when more than one season elapsed without them winning the league.
And although they finished 22 points behind champions Manchester City, Mata believes they will be expected to reclaim their crown next season.
He wrote on his blog: "At United, if you don't win the Premier League one year you know you have to do it the next time, and we will get ready for that. I believe it's fair to congratulate Manchester City for winning for the title. We will try to bring the celebrations to our side the next year."
Mata rounded off the season with his sixth goal in six games, a free-kick to equalise against Southampton on Sunday, but United ended the campaign in their lowest league position since 1990.
He added: "The goal helped the team to avoid a defeat in Southampton, although the score and our final position on the table is nothing we feel proud of."
The Spaniard was marginalised at Chelsea before joining United in a club record 37.1 million-pound move in January, meaning he has played fewer matches than usual and he said: "The 31 games I've played this season have not been enough."
Mata presented the Sir Matt Busby award, given to United's Player of the Year, to his fellow Spaniard David de Gea on Thursday.
He said: "It's the first time that the trophy goes to a United goalkeeper and David deserves a lot of credit for that. He's got amazing qualities and he may become one of the best goalkeepers in the world -- I believe so."