Queiroz, who has played an instrumental role in United's recent successes, left Old Trafford last week to take charge of the Portugal national side.
'It's always sad to see people leave the club and Carlos was obviously a big part of things here," Carrick said.
Carrick: Already missing Quieroz's influence
'He had a big say in the running of the club with the boss, but he has left to do something different.
'As players we can appreciate that and we wish him all the best.'
The Barclays Premier League and European champions returned to action with a pre-season friendly win at Aberdeen on Saturday.
Carrick added: 'We have to earn it all again after last year and we know it's going to be a long, hard season, but we're ready for the challenge.'
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