The Toffees had already been eliminated from the competition prior to kickoff but the caretaker manager still selected a strong side for the encounter.
However, Everton were routed in front of their own fans thanks to braces from Bryan Cristante and Andreas Cornelius either side of a Robin Goosens strike, with Sandro Ramirez netting what turned out to be a mere consolation for the hosts.
"We got ourselves back into the game at 2-1 and looked to make positive improvements, especially at home," Unsworth told reporters after the game.
"It is the story of our season, you can't give away cheap goals. When you put on the shirt you have to play with pride and effort and they didn't do that. That is the big disappointment.
"It was a dead rubber but I spoke before the game and said our fans had paid good money to come and see this. They leave with a bad taste in their mouth and so do I.
"We made a lot of changes. It was an opportunity for the players tonight and they haven't taken it."
Up next for Everton is a Premier League game away at Southampton on Sunday.