Once again David Lowe's squad was very young with six lads from the Under-16 squad involved, and although they battled back to level in the second half, two later goals saw Rovers taste defeat.
After a close opening it was the home side who took the lead just inside 20 minutes. Everton worked the ball inside and although David Raya pushed Tyrone Duffus' shot onto the post, Harry Charsley forced the rebound over the line.
Rovers almost hit back straight away when Modou Cham teed up Luke Wall, but the striker's effort whistled inches past the post.
The two would combine to give Rovers a 55th minute equaliser. A strong run down the wing by Cham saw the ball played through to Wall and he made no mistake with a composed finish for his first of the season.
After that it was Rovers who had the better of the play however it was Everton who regained the lead.
It was a goal that had a hint of controversy about it as there appeared to be a handball in the build-up before a long-rage Callum Connolly's effort deflected off Liam Langford and sailed past a wrong-footed Raya in the Rovers goal.
Rovers pressed for a leveller once more but were caught late on when a free-kick into the box was defended poorly and it was scrambled home by Jordan Thorniley.
Speaking after the match coach David Lowe said: "When we got it back to 1-1 we controlled the game and looked really strong.
"But unfortunately we couldn't make enough of our good play to find that second goal and win the game which is disappointing as we defended poorly for their late goal.
"It was another good learning curve for the lads and a fantastic experience for all of them to play against a top class Academy team.
"We are a young team but it is all about developing players and this should help them in the future, both for the rest of this season and next."
ROVERS: Raya, Doyle (c), Askew, Wharton (sub Edgar 62 mins), Langford, Tanner, Joel, Hardcastle (sub Tomlinson 88 mins), Wall, Edo (sub Howarth 80 mins), Cham.
Subs not used: Williams, Callaway.