Video report by Julia Breen
The delays could be seen from air passengers flying overhead and Mr Houchen told ITV Tyne Tees that some people may have missed flights as a result.
Mr Houchen said: "There is the potential that it looks like one or two families may have missed their flight."
He subsequently took to Twitter to make his apology and commit to a review into the events, with the delays thought to have been caused by a crash on the A66. The mayor also said he would do "whatever I can" to get refunds "or those who suffered major delays or who were unable to attend as a result of the delays".
The Airshow was making a return after a five-year gap and featured several major attractions, including the Red Arrows, the Battle of Britain Memorial Flight and the RAF's Typhoon Display Team.
It was a sell-out, with tens of thousands of people due to attend.
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