Javier Hernandez's 11th-minute goal proved the difference in the 1-0 win, but it was the Reds' dogged display at the back which pleased the manager, as did the impressive performance by Carrick in the centre of the field.
"Keeping clean sheets has been an integral part of our success and we have been careless with our defending," he told MUTV.
"A few weeks ago there was genuine criticism about the defending and the chances opponents were getting. Swansea didn't really make any chances apart from the miss they had in the first half.
"It was a solid performance and we never looked like losing the game. We were comfortable and had good possession. And when you win these games 1-0 it brings the concentration back to a good level which has been lacking. The concentration we showed today is exactly the concentration we need back in the team.
"We've tightened things up and there were some good performances by our defenders. And Michael Carrick was outstanding. I thought he did really well - it was a big performance from him.
"To get Michael back to that form and have the likes of Ryan [Giggs] available gives us good options. We also brought on Fabio, Fletcher and Valencia which shows you the strength of the squad - they were good changes at important times in the game.
"The squad we've got now is strong and I can make changes with confidence and that's very important at this stage of the season."