The Men Behaving Badly star was at the height of his fame in 2000 when it emerged he had a relationship with Holden while she was married to Tv funnyman Les Dennis.
The story became a tabloid sensation, and eventually led to the breakdown of Holden and Dennis' marriage.
Morrissey has long refused to talk about the scandal, but he has now opened up about what happened in a candid new interview with Tv newsman Piers Morgan.
In an episode of Piers Morgan's Life Stories, Morrissey says, "I feel sorry for how the situation was dealt with and I feel sorry for how emotional Les seemed to become. It was very difficult for him and for that I'm very sorry... I've since ran into Les a few times and shook his hand. He lives near us in north London."
However, when asked whether he ever apologised to Dennis in person, Morrissey adds, "No, I didn't. I'm not positive over what there is to apologise about. I don't know what the whole situation was, to be perfectly fair to everybody."
The actor goes on to explain why he has never spoken about the affair before: "I think enough was said about it. This was a very short fling. I didn't have representation at the time, in terms of Pr and this was the first time I'd really come under the cosh (under fire)."
When asked what advice he would give to young actors today, Morrissey jokes, "Yeah, don't f**k a game show host's wife."