The Red Devils got revenge for their recent Premier League loss to the Anfield club by progressing to the fourth round of the Capital One Cup thanks to Javier Hernandez's 46th minute goal.
Moyes, who also saw his side lose 4-1 to Manchester City on Sunday, was relieved that his players had the ability to come up with the required result.
"We lost at Anfield a few weeks ago, we lost on Sunday at the Etihad so we had to bounce back, we had to get some good results and I thought it was a really good result tonight," he told Sky Sports 1.
"It gave me a chance to see a lot of different players playing who've maybe not played as much as they would have liked so it's given me some food for thought.
"I thought some of the performances were really good."