The Red Devils failed to breach a resolute Black Cats as the home side tried to keep their slim European competition chances alive, but could also not find a winner.
The result seals third spot for United but ends a three match winning streak while Sunderland occupy 12th position on the table.
"It was a tough game. Credit to Sunderland, we knew it'd be tough coming here anyway," said Carrick in the post match interview.
"We were a bit too deep at times and wasn't at our best. But to take something from a game when you're not at your best, that is a good trait what we're trying to build as well.
"There were obviously changes, sometimes we were trying to find our rhythm a little bit. I still quite liked a lot of the things that give us a foundation to play better at certain times. To take a point and a clean sheet is okay."
United face Nottingham Forest next Sunday before ending the season away to Brighton and Hove Albion.
Pep Guardiola has said he will make a late decision on the fitness of Rodri and Abdukodir Khusanov ahead of Manchester City's crucial Premier League clash with Crystal Palace on Wednesday night.
Former Manchester United defender Jaap Stam has backed the idea of a swap deal involving Marcus Rashford and Rafael Leao as uncertainty continues to surround Rashford's long-term future.
Mathys Tel endured a dramatic night in North London as his brilliant goal was cancelled out by a costly mistake in Tottenham Hotspur's 1-1 Premier League draw against Leeds United.
Harry Maguire believes Leny Yoro and Ayden Heaven are set to develop into Manchester United's long-term centre-back pairing, insisting both young defenders have amazing potential.
