The Dane has revealed he is "deeply disappointed" with the club's decision to fire him and says he wants to know the full reasoning behind the sacking.
The Dane's tenure at the Liberty Stadium came to an end on Tuesday, with the club just two points above the relegation zone after picking up one win from the last 10 top-flight matches.
Laudrup's stint had been largely successful, and the club remains in the Europa League, which it qualified for by winning last season's Capital One Cup.
The 49-year-old believes he could have arrested the club's poor league form and is now taking legal advice regarding the manner of his sacking.
"I am deeply disappointed to have been dismissed as manager of Swansea City," said Laudrup in a statement released by the League Managers Association. "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.
"Until we receive the response I am unable to say any more about the termination but I do want to take this early opportunity to thank the Swansea City fans for their continued support and say it has been an honor to manage this great football club.
"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."
Garry Monk has taken temporary control at Swansea and faces a baptism of fire when the Welsh outfit hosts rival Cardiff City on Saturday.