Honduras forward Jerry Bengtson scored the lone goal in the seventh minute, knocking a header past Spain goalkeeper David de Gea.
It was an intense match packed with heated aggression. Spain players picked up seven yellow cards and Honduras six.
"The team was tense from the beginning because they knew that they had to score to qualify for the next round," Spain's coach Luis Milla said. "And the early goal made it harder."
Spain's under-23 team has been under enormous pressure to follow in the footsteps of the senior side, which has won the 2010 World Cup and 2012 European Championship.
When asked if he thought the pressure affected the team, Milla said, "Yes, it's possible that the pressure was there, but they are players who play at the highest level.
"The coaching staff has to analyze what led to the elimination. We have to find out what happened."
Besides returning home without a medal, Spain could find itself in the awkward position of coming back from a major tournament without a goal if it doesn't score in the last match against Morocco on Wednesday in Manchester. Spain also lost 1-0 to Japan on Thursday.
Honduras is now second in Group D with four points, two behind leader Japan.
Honduras coach Luis Fernando Suarez admitted his team was lucky to come out of the match with all three points.
"Things went our way tonight, because Spain could have come back to tie or win the game," Suarez said. "We have to remain calm as we look to qualify, because the next match will be very hard."