The Toffees lost 2-1 to Championship side Leeds in the Capital One Cup earlier in the season and Moyes was taking no chances for the third round tie with Cheltenham.
A near full strength line-up was in action at the Abbey Business Stadium with goals from Nikica Jelavic, Leighton Baines (penalty), Leon Osman, Seamus Coleman and Marouane Fellaini securing a 5-1 triumph.
Moyes said: "I don't know if it was the strongest Premier League side put out this weekend or not but it could be folly if I had picked up injuries.
"Then it would have been made to look a bad decision. But I was disappointed when we lost our League Cup tie to Leeds United. I gave a few players a go and I didn't think we came up to scratch.
"I wasn't going to take a second chance, that's for sure. I just felt we needed the people tonight who knew what was going on.
"It was a very professional job. We did a job. I wanted to try and progress in the Cup if we can. We've got a bit of momentum and we want to try and keep it going if we can."
Moyes even included full-back Baines despite him having to nurse an ankle injury.
"Leighton has got a bad ankle problem which I need to watch and be careful with that," the Scot added. "I thought we needed him because we have to respect the players at this level as well and what they offer to the game.
"It was really important we didn't treat it any differently."