Powell was left stranded after being booked on a flight to Scotland to take part in a wheelchair race.
The 39-year-old said: "I've flown all over the world and this has never happened before.
"I was angry and embarrassed."
Powell even offered to get out and use his arms to ease himself up the steps of the Eastern Airways aircraft at Bristol.
But staff again refused to let him board.
Powell, of Carmarthen, who broke his back in a motorcycle accident when he was 18, added: "It's discrimination.
"They told me, 'You can't come on unless you can walk'."
Last year Australia's Paralympic marathon champion Kurt Fearnley received an apology from Jetstar after they made him check his personal wheelchair in with his luggage.
He then hauled himself across the terminal at Brisbane Airport and onto the plane.
A spokesman for Eastern Airways said: "The booking said Mr Powell was able to climb steps unaided.
"But that wasn't the case and he was refused boarding on safety grounds.
"Wheelchair assistance is available as long as passengers can walk up the steps unaided."
Powell later flew to Edinburgh with easyJet and was driven to the 10 kilometres event in Balmoral.