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."