Hooker Callum Young scored Warriors' only try of the day before half-time but the visitors stepped up their game after the break.
Academy Manager Mark Hewitt said: "We took on a very talented Leeds outfit with the majority of the side being part of their successful AASE programme.
"We started the match well but we couldn't match them in the contact area of the game.
"We worked hard to stay in the match until half-time and it was a well-worked try from Callum who scored from the lineout."
In the second-half, Warriors Academy lock Shay Kerry left the field with a suspected neck injury but has since recovered.
Hewitt continued: "Shay went off in the second period and Leeds really came into their own.
"Although they ran away with it, we worked hard against a strong team and there were some notable performances from Andrew Kitchener and Andrew Boyce."
The Under 18s are up against Newcastle Falcons this Saturday in the last game of the season at Broad Street (kick-off 1pm) where they will be searching for their first win of the campaign.
Hewitt added: "If we can get a result from the match it will show significant improvement from last year's showing.
"We have played sides like Leicester and Leeds this season who have had significantly more contact time with their younger players and that is something we are looking to improve at this club."