The striker scored the only goal of the game just five minutes before the break following goalkeeper Nick Pope' s mishap.
The England international appeared to have collected Joe Willock's cross into the box, but the ball broke free after an unfortunate collision with Newcastle United defender Fabian Schar.
Wilson took a touch, taking both Pope and Nathan Collins out of the equation, before lifting the ball into the roof of the net, over the back-tracking Chris Wood.
"At the time you think it is a possible foul but having looked at it after the game, it is a clumsy challenge but not necessarily a bad challenge," said Dyche.
"It just bounced out of Pope’s hands after he took it so well. Their player reacted quickly and it was a good finish.
"Some of the quality was really pleasing but goals change the feeling of games, not just the scoreline, and I felt it did for them.
"It gave them something to fight for and hang onto and changed the feel in the crowd."
The Clarets had chances in the first half but, yet again, failed to capitalise as the Magpies went on to claim their first win of the campaign, while moving level on points with Burnley in the process.
Johann Berg Gudmundsson's deflected attempt cannoned off the outside of the post, Maxwel Cornet's header was well saved by Martin Dubravka and substitute Matej Vydra squandered a golden opportunity when chesting down Gudmundsson's pass in acres of space.
Dyche said: "In the first half I thought we were really good. We came here and took the game on, we opened them up on occasions and created good quality moments and chances without taking them which is a question mark of our season.
"That continues to be a challenge for us, those cutting edge moments and trying to find a way in that top third.
"That is the challenge that’s ahead of us because generally the performance was solid and organised.
"There were some good individual performances."
Jay Rodriguez had a goal chalked off in the second half, but that was as close as it got for the Clarets, who failed to test Dubravka after the break.
"We obviously scored a goal which was rightly offside but it was some very good play," Dyche concluded. "Right at the end Dwight put in a couple of great crosses but we couldn’t get on the end of it.
"It is a really frustrating one but it has been like that this season where we have never been a million miles away but are not finding the key moments."