Markle also added that Harry was "quite easy to talk to" and that the two have had discussions about politics, including a conversation in which Markle complained about President Donald Trump shortly after the US election.
He also recalled the one condition he placed on the prince when Harry rang Mr Markle in Mexico to ask permission to marry Meghan.
After Thomas decided not to attend the wedding, Harry's father, Prince Charles, stepped in to accompany Meghan down the aisle at St George's Chapel at Windsor Castle and her dad felt "honoured" with the replacement. "Yeah, he's great. He's an interesting guy, but my daughter's been a princess since the day she was born".
Though Thomas Markle has not met Prince Harry face to face, they talk politics on phone and he thinks that the Prince is "very nice man, gentleman, and very likable".
He told his daughter that he wouldn't be able to make it for her big day before going into surgery, admitting the conversation was a hard one.
Days before the wedding, Thomas received flak for staging paparazzi photos, which led to the speculation that he was embarrassing his daughter.More news: Things that must happen for a Kawhi Leonard trade
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Photos of Markle intently studying "Images of Great Britain: A Pictorial Tour Through History" in a Starbucks quickly went viral - but were later discovered to have been staged.
"I think he was open to the experiment", added Markle.
"I realized it was a serious mistake", he said of the paparazzi pictures.
"Meghan cried and they both said "take care of yourself, we're really anxious about you", Thomas said. "I had been seen as negative for an entire year".
It comes as Thomas revealed how he cried while watching Meghan get married on TV, after a heart attack prevented him from travelling to the United Kingdom for the big day. I sort of disagreed with that but I still like Harry. "I couldn't have been more proud", he said. However, Thomas noted that he'd agreed with Meghan's decision not to invite other members of their family to her wedding, saying that "she would have offended the others" who weren't invited.
He claimed Harry once told him to "give Donald Trump a chance". "I have my politics", Markle, 73, told the British morning show.
"I was complaining I didn't like Donald Trump, he said, "Give Donald Trump a chance", continued Thomas. "That upsets me somewhat".