The Magpies twice battled back from behind but conceded within two minutes of their first equaliser and one minutes of their second as Howe's side sunk to their fifth Premier League defeat in their last six games.
The defeat leaves Newcastle in 12th place and 12 points adrift of the top five and Champions League places.
United hoped they'd turned a corner after an upturn in performances in cup competitions of late, but they continue to be plagued by inconsistency.
Howe said: "Hugely frustrated. We think we're a good team and we think we've got every opportunity to grab games and go on a really good run.
"The team is in a much better place in terms of a general performance than it was at the start of the season but we're not putting it together for 90 minutes, even in games. That's a huge frustration.
"We were dominant in that second half, score and then self implode in a couple of seconds. It's hugely frustrating for everybody. Only we can look to improve that with proper analysis."
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Jarrad Branthwaite headed Everton ahead after 19 minutes. Jacob Ramsey levelled for the Magpies but Nick Pope gifted a second Everton goal for Beto two minutes later.
Substitute Jacob Murphy equalised with eight minutes to play but just a minute later Everton substitute Thierno Barry bundled in what proved to be the winner.
Newcastle started with Nick Woltemade in midfield, Joelinton left wing and Anthony Gordon up-front but the Magpies were dreadful in the early stages, prompting Howe to shift things around after just half an hour.
He moved Woltemade up-front, Gordon to left wing and Joelinton into midfield.
Howe said: "I always say on these things that it would be foolish of me to say I regret the set-up.
"It was done with reason and with the limited time we had to prepare for the game I thought there was good logic.
"Then you see the reality and we didn't like it, so we changed it.
"I don't know, I think sometimes too much can be made of those things. It's a really small tweak in terms of positioning. The biggest one would be Anthony moving out wide to get his speed against one of the defenders.
"That's probably the biggest change. The other two are minimal.
"You can always look back and then reflect and say, would I do that again? That's a different question. That's the perils of being a manager."
Newcastle were forced to make a substitution at the start of the second half when Joe Willock replaced Jacob Ramsey, who was sick on the pitch.
Howe said: "It looked like an illness.
"The first I was aware was half-time. He felt like he could continue but it was obvious at the start of the second half he couldn't."