The 26-year-old, who was included in the PFA Team of the Year and finished second behind Gareth Bale in the PFA Player of the Year award, scored 30 goals in all competitions for the Reds this season.
The latter part of his season has been marred by his 10-game ban for biting Chelsea's Branislav Ivanovic, which will stretch into next term, and Suarez wanted to thank the fans for their support throughout the campaign.
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"It breeds a comfort and everyone knows where they stand, you can get a bit of continuity."
After celebrating at fifth Premier League winners' medal last season with the Red Devils, Carrick insists the players are already looking forward to defend their crown next term under new boss Moyes.
"What's done is done now," added the former Tottenham and West Ham midfielder. "We've moved on from that already, looking towards these games and next season, you can't look back for too long.
"You can enjoy it, we've enjoyed it, we've celebrated, but we've celebrated enough now and it's time to move on."