The Dane was sacked on Tuesday following a poor run of form by Swansea, 12 months after leading the club to the first major trophy in their history.
The League Managers Association (LMA) is now writing to the club to ask for the reasons for his sacking.
Laudrup said in a statement: "I am deeply disappointed to have been dismissed as manager of Swansea City.
"In particular, the manner in which it happened and the actions the club has taken since notifying me in the briefest of letters which gave no reasons why such hasty and final action was deemed necessary.
"I am, of course taking legal advice and the LMA have already written to the club asking for a proper explanation as to why I was summarily dismissed."
Laudrup also revealed he has been banned by Swansea from visiting the training ground to thank the players.
He added: "The club has informed me that I cannot visit the training ground to say my farewells to the players so I do that now through this statement.
"The players have been fantastic and their contribution under the very professional guidance of my coaching staff has been absolutely fundamental to the club's recent successes. Three members of my staff have also been dismissed.
"Whilst league results have been disappointing of late, we are still 12th in the table and it is there for all to see the fine margins in the league this season in terms of points that separate 11 clubs.
"Although we have been unfortunate with injuries, I believe our league form would have improved and that we would have benefited from the forthcoming Europa League and FA Cup matches."
Swansea have picked up just six points from their last 10 matches and are two points above the relegation zone heading into this weekend's derby showdown with Cardiff.
The Swans, however, are through to the fifth round of the FA Cup, where they face Everton, and are also in the last 32 of the Europa League, with Italian side Napoli their next opponents.
Former Real Mallorca, Spartak Moscow and Getafe boss Laudrup said that he was proud of what Swansea had achieved under his management since taking charge in 2012.
He said: "I have thoroughly enjoyed my time managing in the Barclays Premier League which I consider to be the one of the best leagues in world football.
"I leave the club proud of our collective achievements over the past 20 months and I believe we have continued the club's progression in the manner of my predecessors including Roberto Martinez and Brendan Rodgers.
"Of course the obvious highlight during my time in charge was leading Swansea to the first major trophy in the club's history in winning the Capital One Cup at Wembley resulting in European qualification.
"In addition, our ninth place in the Barclays Premier League was our highest finish in 31 years and the second highest in the club's 102-year history which again is something which fills me with pride.
"This season we have all enjoyed the memorable journey in the Europa League where the team will soon to face Napoli in the last 32 of the competition.
"I wish the club the very best for the future and for the rest of the season in the Barclays Premier League, Europa League and the FA Cup."
The 49-year-old ex-Denmark, Real Madrid, Barcelona and Juventus player left Swansea with immediate effect on Tuesday following a decision that chairman Huw Jenkins said was ''taken reluctantly''.
Veteran defender Garry Monk and first-team coach Alan Curtis have been put in charge of the team ahead of Saturday's clash with rivals Cardiff.
Jenkins said: ''It is a decision we have taken reluctantly, but it's a decision made in the best interests of Swansea City Football Club and our supporters.
''It is the first time in nearly 10 years that the club has parted with a manager in this way, but we had to remove the constant uncertainty surrounding the club and Michael's long-term future with us.
''I had a meeting with Michael today in a final attempt to support him and establish a way to improve the work of the backroom team to secure the results we need over the final 14 Premier League games.
''However, after thinking long and hard about the best way forward, I felt it was unlikely we would achieve a stable environment at the club to allow us to get back to basics and produce the performance levels that have served Swansea City so well over the last few years.
''Now we need to put that uncertainty behind us and move forward as a united football club on all fronts, while placing on record our gratitude to Michael for the work he has done over the last 18 months and wish him well for the future.''