Welbeck scored for only the second time this season when he climbed above Sergio Ramos to give Manchester United the advantage in their Champions League draw with Real Madrid on Wednesday.
The tally compares badly alongside Robin van Persie's 23 goals and the 13 and 14 scored by Wayne Rooney and Javier Hernandez respectively.
But Carrick does not believe the statistics do justice to Welbeck's overall contribution.
"If the team is winning, who is scoring is not such an issue," said Carrick.
"Danny has all the attributes to be a top player but probably doesn't get the credit he deserves.
"As a Manchester lad, he loves the place. He is genuine and gives everything.
"He worked so hard again against Real."
- Sports & Recreation
- Manchester United
- Real Madrid
- Sergio Ramos
- Wayne Rooney