The Magpies completed a move to sign the New Zealand International after activating a release clause in his contract believed to be around £25million.
Wood made his Magpies debut less than 48 hours after completing his move to Tyneside and is set to be a key player as Eddie Howe looks to guide his side out of the Premier League relegation zone.
Clarets boss Dyche reflected on losing the 30-year-old frontman and admitted the release clause made the deal “straightforward” for the Magpies.
He said: “It happened quickly, when there was a release clause they know what it is, which they obviously did, and they activated it.
“Then it is a straightforward contractual situation other than medicals and stuff like that.
“It is irrelevant. Someone knew what the clause was and they activated. He could have gone to anyone who is willing to meet it.
“That is the way it goes, you don’t want to lose good players at any time.
“If a contractual situation opens up and the player chooses they want to go then that is just a fact of contracts and the delicacy of them sometimes.”
Dyche revealed he had no issue with Wood’s decision to swap one relegation battle with Burnley for another at Newcastle.
The striker was a popular figure at Turf Moor after scoring 53 goals in 165 games during a five-year stay with the Clarets.
Wood suggested that a key motivation for his move to Tyneside was that he felt he was in the “comfort zone” with Burnley.
Dyche took no exception with the comments and praised the striker for doing a “very, very good job” for his club.
“He has been performing for a long time and sometimes players do hit a quiet spell,” he said.
“It certainly wasn’t us allowing him to sit in his comfort zone.
“I understand him slightly, maybe he feels he needs a freshness and a difference.
“I found him an honest fella who knows when he is not doing as well as he can do.
“He knew he was quieter than what we expected from himself and from us.
“It was a clause in a contract, we weren’t pushing that to happen.”
He continued: “He is a professional footballer, has done very well for the football club, an opportunity arose and he thought it through and decided it was right for him. That is football and being an individual footballer.
“There is absolutely no question marks in my mind at all, for what he has done here, the goals he scored, the way he performed, the way he has conducted himself and the way he has attempted to be successful here.
“He has been quieter this season than previous but generally he has done a very, very good job here.”