The defeat coupled with Atalanta’s 1-1 draw against Apollon Limassol means the Toffees cannot progress from the group stage with two matches remaining.
Unsworth, who was promoted from the club’s academy to become caretaker boss after the sacking of Ronald Koeman, has now lost all three games he has overseen.
Former Chelsea player Bertrand Traore opened the scoring in the 68th minute when he outpaced the Everton backline and slotted past Jordan Pickford.
Their second came 14 minutes from time when substitute Houssem Aouar threaded his shot past the reach of the England goalkeeper, who was already spread out on the turf having saved from Mariano Diaz in the build-up.
It went from bad to worse for the visitors when they were reduced to 10 men after Morgan Schneiderlin received a second yellow for a foul on Maxwel Cornet.
And with two minutes remaining former Manchester United midfielder Memphis Depay, who set up the strike for Aouar, applied the final blow when he headed in the third from six yards.
Earlier in the match, Everton full-back Cuco Martina was taken off in a neck brace having fallen awkwardly in a challenge with Cornet.
