Harry's press office declined to comment on Markle's televised interview, which could raise eyebrows because senior royal figures are scrupulously careful not to comment publicly on domestic or global political affairs.
He told ITV he was "doing much better" and that he regretted missing the big event. "I sort of disagreed with that".
Prince Harry was ever the gentleman as he caught Meghan Markle after she stumbled in her heels on Saturday.
'The unfortunate thing now is that I'm a footnote in one of the greatest moments in history instead of a dad walking his daughter down the aisle. "That really upsets me somewhat".
Markle also spoke of the moment Prince Harry asked for his daughter's hand in marriage over the phone.
Markle went on to give details of how his 36-year-old daughter had told him she had a boyfriend, and that he was British, before admitting it was Prince Harry.
In the run-up to the wedding Mr Markle became embroiled in a controversy over reports he had staged paparazzi photos of himself in wedding-related activities, such as being measured for a new suit.More news: No need to justify family separation of migrant children: Steve Bannon
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He said: "I look forward to coming to London to meet them soon". "Meghan cried ... and they both said "take care of yourself, we're really anxious about you". Her flowing, floor-length wrap dress in a blue-and-white floral pattern by Oscar de la Renta ($5,490, modaoperandi.com) complemented the white fascinator Markle wore atop her signature messy bun and a matching clutch she held in her right hand.
"For the most part it was always, 'Don't speak to the press.' The rest of the things were, 'Just be careful, '" he said. "I feel bad about it", he said.
He watched the wedding from California, where he was recovering from heart surgery.
And in a final word of thanks, he added of Prince Charles, "I can't think of a better replacement than Mr Charles". "I apologize for it and that's all I can do".
"Sadly, my father will not be attending our wedding".
The Duchess of Sussex's dad has spoken for the first time since Meghan tied the knot with Prince Harry last May. "My daughter is capable of anything and she will be a compliment to the royal family".