The Toffees won the first leg 2-1, but goals from Miguel Veloso, Pedro Mendes and Matias Fernandez secured the win for Sporting.
Moyes said: “We never got started. Credit to Sporting, they were the better team tonight and deserved to go through.
“We felt confident but maybe we made mistakes in the first game which let them in. They took their opportunities.
“I didn’t see this result coming. We didn’t play to the levels we have in recent weeks. They worked very hard and ran very hard all night.
“The idea was to go and get a goal. But we found it difficult. We knew the opening 20 minutes would be tough. But we never made anything happen.”