The Toffees boss insisted his side's sluggish performance in the opening exchanges, rather than squad rotation, was the main reason for their League Cup exit
The Toffees came into the match full of confidence, sitting third in the Premier League after getting their campaign off to an impressive start.
However, goals from Aiden White and Rodolph Austin put the Yorkshire side out of sight, despite Sylvain Distin's late header providing hope for the visitors.
After the game the Scot refused to blame the six changes he made as a reason for the Merseysiders' lack of fluency, preferring to point to a sluggish opening period.
"We started terribly, gave them the initiative and lost the game in the opening 20 minutes due to the way we started," he told Sky Sports.
"We gave away a really poor first goal and left ourselves trying to get back into the game. We were not very good in the first half, but we got better in the second, but not as good as we've been playing.
"These boys are in the squad and have to be able to show they can come in and play. If you don't use them, what's the point in having them? The players want to play and be involved.
"It's a chance if you get good draws and you play well. If you get difficult draws it makes it harder and so does not playing well. We had a combination of that."
Meanwhile, Leeds boss Neil Warnock was delighted with his side's performance and was adamant they fully deserved their victory.
"They [Everton] wanted to win it - make no mistake - but I think we deserved it on the night," he said.
"I thought we were a little bit sharper, we won the second balls and I think we should have scored one or two other goals, so we're disappointed that we didn't, but we never do anything easy."