Monk made eight changes to the side which picked up a Premier League draw at Stoke in midweek, but saw Swansea bow out of the FA Cup.
Swansea matched their high-flying hosts for long periods.
Jonathan de Guzman cancelled out an early Lacina Traore goal and Swansea fancied their chances at half-time.
Two Toffees goals in the final 25 minutes dashed those hopes, but Monk defended the decision to shuffle his pack.
"When you have seven games in 21 days it's impossible to play the same 11 every week," said Swansea's head coach.
"Every player has been magnificent in training and I said they would all get their chance.
"Their attitude has been spot on and they deserve that. They have to play — I am true to my word. It's a bit to do with freshness but they deserved a chance.
"It's a squad game nowadays. Everyone seems to be amazed when teams rotate but there are so many games you have to rotate for.
"Every side I pick is to try to win the game and I think even with the changes, you wouldn't have thought that was a team where a couple of the players haven't featured until Everton got their second goal."
Wilfried Bony stayed on the bench as Monk had to factor in Thursday's Europa League clash with Napoli.
Alvaro Vazquez started up front and Leroy Lita made his first appearance in nearly two years from the bench.
"I thought Alvaro was doing well with his pressing. We were still in the game but you can't just go gung-ho because Everton are a good team," added Monk.
"I thought Lita was very good in the last 20 minutes even though we were losing. It was a shame the second goal came when it did because their crowd were starting to get a little bit frustrated.
"The truth is I have only been thinking about the next game. I put a team out I thought could win and for an hour we were right in it. I thought Leroy had trained really well and deserved his chance."
Michu is continuing to work towards a first-team return after recovering from an ankle problem.
Jonjo Shelvey and Alejandro Pozuelo should return to the practice pitch this week, when Kyle Bartley's hamstring injury will be assessed.
The centre-back was forced off after half an hour yesterday, but Swansea are hopeful the issue is not too serious.