The 27-year-old England left-back, who watched a replay of the match on TV on Thursday morning, is adamant he did not intend to hurt Hutton, adding: "I did not mean to go in hard that way.
In this case the referee decided it was a yellow card but we've seen tackles that were much less serious given red cards
Tottenham boss Juande Ramos
"It was high but I tried to read the ball and get the ball first but he was a little bit too quick for me.
"It was not malicious and I am a little disappointed with what people are saying, that I meant it.
"Of course it was a bad tackle at the time but in the heat of the moment you want to win the game and win every tackle. As I said, I am sorry for Alan but it was never meant."
Hutton himself has said that he holds no grudge towards Cole for the tackle.
"He went to win the ball and I've just got there quicker," said the Scot on Thursday.
"I wasn't thinking about whether he would be sent off, I knew the challenge was high but so was the ball.
"I am not blaming him for it, I've probably done a similar challenge in my career. He said he never meant it afterwards and that's fine with me."
Spurs boss Juande Ramos echoed the sentiments of Hutton.
He said: "We are just very happy that no player got injured.
"In general terms it was a clean game and there wasn't any violence."
Chelsea players surrounded Riley after the incident in first-half stoppage-time at White Hart Lane and Cole turned his back on Riley before he was eventually shown a yellow card.
Blues boss Avram Grant added: "I didn't see it but the referee was very close and I saw everybody jump on him, including the Tottenham bench.
"I know when we are doing this everybody says we are not behaving right. We have a lot of respect for referees."
Riley did not include the reaction of the Chelsea players, or that of Cole, in his match report so no further action will be taken on that matter by the Football Association.
The FA cannot take any further action over Cole's challenge on Hutton because the Chelsea star was booked for the tackle.
An FA spokesman told BBC Sport: "The referee saw the incident and dealt with it. We cannot re-referee matches.
"The player was shown a yellow card at the time and the decision is not then looked at retrospectively."
Under Fifa regulations, a decision taken by a referee can only be rectified by a disciplinary committee if the referee sends off the wrong player, or makes an obvious and serious error.
The FA has acted retrospectively to upgrade a booking before, when it suspended Ben Thatcher following his challenge on Pedro Mendes in a game between Manchester City and Portsmouth in August 2006.
But the FA spokesman added: "As we said at the time, that was an exceptional case.
"The reason why Ben Thatcher was charged in addition was because, even if he had been sent off by the referee Dermot Gallagher, we would still have charged him on top.
"That was the rationale we used to charge him with violent conduct."
Newcastle boss Kevin Keegan believes Cole's apology could actually prove to be a turning point in relations between players and officials.
He said: "With the incident in the week, Ashley Cole has come out and apologised - had he not done that, a lot of people would have been very, very disappointed with him.
"But he has been big enough to do that, he has accepted he was wrong and he has said sorry in the only way he can.
"You have to respect that, and maybe that could be seen as a turning point because certainly, nobody likes to see referees being treated with disrespect."
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