A second-half goal from Anthony Pilkington saw the Canaries beat the Red Devils 1-0 at Old Trafford, prompting the visitors to be overtaken by rivals Manchester City at the top of the Premier League.
United host struggling QPR on Saturday and Carrick believes that, despite enjoying a good start to the season, the pressure is on to earn all three points at Old Trafford.
"Of course there is always pressure at Manchester United and you are always expected to win," the midfielder told the Times of India.
|IN ON THE ACTION?|
|18/1||Michael Carrick is 18/1 with PaddyPower to score the first goal in Manchester United v QPR|
The defeat to Norwich marked Carrick's 400th league appearance but the England international had not even been aware of the milestone.
"I hadn't even realised that until someone told me!" he added. "I suppose I have been playing for a number of years and the games do add up but it is not something I look for.
"For me it is more about the trophies, what people win and what they can achieve. Maybe at the end of my career I can look back and see what I have done but, at the moment, it is just about winning trophies for me."