Carrick and United went to Elland Road in desperate need of a win but only managed to snatch a point before heading back over the Pennines.
The draw against Leeds now leaves Manchester United winless in their last six games across all competitions, sitting in 13th in the Premier League table.
Speaking to NBC Sports after the game, Carrick decided to look on the bright side and insisted that it was still a "step forward."
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"Yeah, it was a tough game for both teams, I think. It was one of those challenging games. You could feel there was an edge to the game. It was a good game," he said.
"Maybe if you talk about top quality, maybe it wasn't top, top quality I think we are capable of playing. I think in little moments and spells we played some really good football.
"It's a tough place to come. With the results we've had, we weren't quite flowing, but there's enough in there to take from it. We had to work for it. I was proud of the boys for the way they went about it in difficult circumstances.
"A point is a point. It is a step forward for us."