Jonathan de Guzman cancelled out Lacina Traore's early opener, but mistakes from full-backs Neil Taylor and Jazz Richards saw Roberto Martinez's men re-establish their lead and book their place in the quarter finals.
Taylor's misplaced pass was seized upon by Steven Naismith for Everton's second, before Jazz Richards felled the Scot in the penalty area, allowing Leighton Baines to find the net from the spot.
"We were well in the game," said Monk. "We finished the first half positively after going a goal down.
"Unfortunately, we made a couple of mistakes, which is frustrating. But they were honest mistakes, and I can accept them.
"The players are their own biggest critics, and they don't need to be told.
"The first goal was a set-piece and we didn't deal with the second ball. We reacted well and if you look at the first half, we had two or three really good chances. If they go in, it could be a different game.
"Neil then makes his mistake and Jazz then brings Naismith down for a penalty. But apart from them, we were well in the game.
"They weren't cutting us open and having shot after shot. It was just individual mistakes."
Explaining his decision to name a heavily weakened starting XI for the trip to Goodison Park, Monk added. "When you have seven games in 21 days, it's impossible to play the same team every game.
"It's a squad game. With Europe, you have to have that rotation. I won't rotate for the sake of rotating.
"Until we conceded the second, you wouldn't have believed we made eight changes."
Swansea host Serie A outfit Napoli in the first leg of their UEFA Europa League round-of-32 tie on Thursday.
