The Dane, who led the Liberty Stadium outfit to the League Cup title last season, qualifying for the UEFA Europa League in the process, was dramatically relieved of his duties earlier this month and replaced by defender Garry Monk.
Having claimed to have waited nine days to receive written notification from the club, Laudrup spoke about the circumstances of his departure for the first time on Tuesday.
"Mid-January, I'm told they're not satisfied and that's that," he said. "They want to change the coaching staff. We talk about it; I always want to listen but don't agree with what's said.
"After that we play a cup game, which we win (2-1 at Birmingham City); we play a league game; we win (2-0 at home to Fulham), and we have the last game against West Ham (that) we lose (2-0 at Upton Park).
"After that I get another message - I should really, really, really change staff.
"My answer is we already discussed that but we agree to a meeting on the Tuesday.
"I had a personal matter on Monday morning. I wasn't in Paris (as had been widely reported). It was a personal matter and the chairman knew about it.
"On Tuesday, we had a meeting again about staff and changing staff. I say we have already talked about it and think it's a big mistake to talk about it because it's in the week of one of the most important games - the Cardiff game.
"I shake hands. They say thanks for the work you are doing. Then, Tuesday afternoon, I receive (a) mail to say that, due to breach of contract, it will be terminated just a few hours after the meeting.
"I'm very, very confused so I call and ask what's going on. It was a little difficult to hear what was said on the phone. I said, 'by the way, what does breaches mean?'. They didn't really know."
Laudrup, who also revealed a number of his close-season transfer targets failed to materialise, is considering legal action against the club as he looks to resolve the matter of compensation, but the 49-year-old insists he has not been put off managing in the Premier League.
"It wouldn't be fair to the UK to say it's soured my relationship with British football," he added. "Of course I would like to work in (the) Premier League and win more trophies.
"There's never been anything (that) said I would move on. I was planning on staying next season as well. I had one more year."
Swansea host Napoli in the first leg of their Europa League round-of-32 clash on Thursday.
