The Merseyside club held a slender 2-1 lead from the first leg at Goodison Park last week, but were hammered 5-2 in Ukraine on Thursday to ensure there are no English sides remaining in European competition this season.
Andriy Yarmolenko opened the scoring with a 25-yard screamer, and although Romelu Lukaku levelled with an excellent effort of his own, goals from Lukasz Teodorczyk and Miguel Veloso put Dynamo 3-1 up half-time.
Oleh Husyev, scorer of Dynamo's sole goal on Merseyside last week, then added a fourth before Antunes added to Everton's misery with a stunning long-range strike, making Phil Jagielka's late goal scant consolation as the Premier League side slumped to a 6-4 aggregate defeat.
Despite Everton's defensive frailties, Martinez said the whole team should take responsibility for their crushing defeat.
He said: "The back five have been very strong in the last two games - the same back five only conceded one goal in the last two games from a corner in the first leg against Dynamo - and kept a clean sheet against Newcastle.
"I felt the communication experience between them would be important today. Both teams used the pitch in a good manner but the whole team didn't defend well enough.
"The second goal started from an attacking corner and sometimes those situations you can't completely control in the game. It wasn't a case of the personnel, I felt Dynamo built momentum with the home crowd and capitalised on that."
"A couple of times we made some defensive mistakes but there was also some incredible finishing from the opposition. Some of the goals, it would be difficult to see them again in the same game."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.