Moyes selected a reasonably strong side while taking the opportunity to give some players match time and try out a couple of positional experiments.
He said: "We needed to see where Victor Anichebe was fitness-wise and James McFadden. We wanted to see how the young boy Magaye Gueye could play.
"Landon Donovan's still coming back into it. A lot of people have said (Diniyar) Bilyaletdinov is a central midfield player so we gave him a chance in there.
"Marouane Fellaini's just back from injury, Seamus Coleman got a chance to play at right-back and I wanted to rest Leighton Baines."
Moyes ended up having to play Baines for the final half an hour after Coleman aggravated a thigh problem, and he added: "I thought even in the 30 minutes you could see the difference of what a top English player looks like.
"When he came on he really lit up the stage."
Donovan played his second game since returning to the club for a second spell on loan from Los Angeles Galaxy and almost opened his account with a long-ranger late on that hit the woodwork.
McFadden, meanwhile, started a game for the first time in more than a year.
The Scot left Birmingham in the summer after a season wrecked by a serious knee injury and had made only two brief substitute appearances since rejoining Everton in October prior to yesterday.
Moyes said: "Landon's played in two of the performances I wouldn't put near the top of our hitlist, that's for sure, so we could have done with helping him a little bit more. But I thought there were glimmers of good things from him.
"You could see James needs the games. He's had bits of reserve games but there's a big difference no matter who you play when you come onto the big stage and there's a crowd.
"He had a couple of chances to score, which he might have been hoping to finish off."
Tamworth boss Marcus Law, meanwhile, has challenged his side to push for Football League status after watching them once again punch above their weight in the FA Cup.
The Lambs have become regulars in the third round since reaching it for the first time in 2006, when they took Stoke to a replay before eventually losing on penalties.
The following year they went out to Norwich and on Saturday they got their first crack at a Premier League side when they and 6,000 fans headed to Goodison Park.
Johnny Heitinga gave the hosts the lead inside five minutes, but Tamworth made life difficult for David Moyes' side for long spells before Leighton Baines sealed a 2-0 win from the penalty spot.
Law, whose side are currently 14th in the Blue Square Premier, said: "What a fantastic experience for all those boys.
"I'm not only proud of the players, I'm proud of the club, how we've dealt with this situation, from the exposure to bringing 6,000 supporters here, and it's got to be a foundation now to move on and progress up the league.
"Like every club that exists, we want to be as near to the Football League as we can, if not in it."
Tamworth made their presence felt on and off the pitch with their noisy fans offering tremendous backing, and Law is hoping the experience will encourage them to come and support the team in the league.
"I think the fans were singing when they got here at 10am," he said. "The town can be very proud. What I've got to do now is try to get as many of those 6,000 people in at The Lamb.
"I don't know if we can contain 6,000 but the league is a good product. If you look at the results (yesterday) from Wrexham and Fleetwood, it's a good standard. There's some excellent coaches and managers and some excellent players.
"Hopefully the Tamworth supporters have seen the difference between the Premier League and the Blue Square Premier is a dubious penalty and a set-piece, so why not come and watch us on a Saturday at The Lamb rather than travelling all across the country?"
