The Red Devils were humbled at the Etihad Stadium but recovered to eliminate old rivals Liverpool, and Luis Suarez, from the Capital One Cup thanks to a goal from Chicharito
The Scot made a number of changes from United's 4-1 loss at the Etihad Stadium, with Shinji Kagawa, Nani and Chicharito among those given a chance to impress.
The Mexican striker took his opportunity, smartly volleying home a corner early in the second half to hand United a 1-0 victory, and Moyes was glad to see his players come out fighting.
"We had to try to come out and show something a bit better than we had done [against City]," he told Sky Sports.
"We had to bounce back and I thought it was a good result. It's given me a chance to see some players I haven't seen much and it's given me food for thought."
Moyes was particularly impressed with Chicarito, and praised the 25-year-old's movement in the lead up to his winning goal.
"The movement is great for the goal," he added. "That's what Chicharito is all about. He finds space so well."