Coleman, who guided Wales to the semi-finals at Euro2016, was approached by the Tigers for their vacant managerial position which was made by Steve Bruce's sudden exit.
However, the Wales FA turned down their approach on Tuesday which has delighted Clarets star Vokes who is keen to continue working under Coleman at international level.
"The gaffer has been a massive part of what we're about with Wales and to see that he is staying is great news," the Wales forward told Sky Sports.
"Hopefully that can help us going into the World Cup campaign."
The 26-year-old, who scored in the quarter-final win over Belgium, also lauded Coleman's efforts with the national team since his appointment in 2012.
He added: "He's been great. We had some tough times with Wales, obviously when Gary Speed died it was a tough time and for Coleman to come in, it was hard.
"As a squad, we went through some tough results and tough games, but we came out the other side of that and I think that's what probably built us as a squad and him as a manager.
"So to all come through that, get to the other side and get the rewards of this summer has been massive for us.
"He's great with the lads and gets on well with everyone. We have a good craic, but we know when to work hard and we do.
"There's a lot of off-the-field stuff that we work hard on as well with the coaches and the managing staff in the classroom. I suppose it all pays off when we get out onto the pitch."
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