David Moyes felt a poor start cost his side after their Capital One Cup hopes came to an end at Leeds.
The Blues conceded inside four minutes at Elland Road and fell two goals behind before Sylvain Distin grabbed a late consolation.
"We started badly and gave Leeds too much encouragement and because of that we ended up paying the cost," said Moyes. "We were disappointed because we were trying to get through in the cup.
"It was always going to be tough. We're not massively endowed in terms of the players who are available to us but I thought tonight we could still put out a side that could win the game. The first half was as poor as we've played this season."
Moyes made six changes to the side which eased to victory at Swansea on Saturday with midfielder Francisco Junior handed his first-team debut and summer arrival Bryan Oviedo drafted in for a maiden start.
Jan Mucha, Steven Naismith, Sylvain Distin and Magaye Gueye were also included in the starting XI, and Moyes said: "We gave some players an opportunity. We have a squad of players and we have to use them. You have to have a squad of players and when you get chances you have to give them games. We did that and one or two didn't do as well as they can do."
It all added up to a very disappointing evening for Everton's 5000 travelling supporters and the manager added: "If you looked at the team we put out tonight you would be disappointed if it didn't come and get a result. But in the first half we just didn't put in a good enough performance.
"I'm really sorry we weren't able to get the fans a result."