"I would like to say that no harm was meant to the Iranian people or its territories whatsoever. I hope that this experience will help to build the relationship between our countries."
He said their captors met all their needs and they were "treated with a great deal of respect and dignity".
"I would just like to thank on behalf of my team the Iranian people for looking after us so well," Carman added.
Captain Chris Ayre said the Iranians respected "all our rights" and they were given medical and physical care, "plenty of food and water".
"No one has been harmed in any way, just wanted to make sure that some rumours have been going round and just tell them that they are untrue.
"Every one is in good health and in good spirits now that we have been freed," added Ayre, thanking Ahmadinejad for "his tolerance and kind attitude".
"Every one is in good health and in good spirits now that we have been freed"
Captain Chris Ayre
He was especially thankful to "people at the non-governmental organisation who have been instrumental in securing our freedom".
The brief interviews were aired late on Wednesday on Iranian state television.
Ahmadinejad first gave a medal of honour to the commander of the Iranian coast guards who captured the Britons before making the unexpected announcement to release the crew.
He also mocked Britain for sending a mother, Leading Seaman Faye Turney, on such a dangerous mission.
Turney told Iranian television "it was a strange feeling" and that she was "embarrassed to start off with" when she heard the comments.
She then added: "It was nice that he has actually taken it into consideration and realises what some of us do for our jobs."
Turney also thanked Iranians "for letting us go and we apologise for our actions, but many thanks for having it in your hearts to let us go free".
Describing her detention, she said the Iranians "were fantastic" and that they had not been harmed in any way.
"It was nice that he has actually taken it into consideration and realises what some of us do for our jobs"
Leading Seaman Faye Turney
"No one hurt us, we were well looked after, well fed, well watered the whole way through," she added.
But she added: "It would be nice to get back, get home and see my family.
"The treatment here has been great, but it will be nice to get back, get home and see my family."
And celebrations will be awaiting her and her crew mates at home.
Yellow ribbons hung on the walls of local pubs on Britain's south coast where the crew is based as families gathered around on Wednesday to watch a press conference where Mahmoud Ahmadinejad, the Iranian president, announced the crew would be freed.
Sandra Sperry, mother of 22-year-old marine Adam Sperry, one of the 15 captured, said: "I'm absolutely ecstatic. I can't believe this is happening. I never expected it.
"I thought this would go until the end of next week at least," she said.
A vigil planned for Friday at his local pub in Leicester, central England, would now be a party.
Perry's uncle, Ray Cooper, did not seem to care whether Iran or Britain had come off looking better in the standoff.
He said: "Whoever has been in the right or wrong, the whole thing has been a political mess, so let's just get them home."
The crew is expected to land in London on Thursday afternoon.
April Rawsthorne, the grandmother of 21-year-old sailor Nathan Summers, said: "I am just so happy today."