A second-half goal from Jan Vertonghen was enough to beat a Swansea side who came to White Hart Lane looking to keep things tight at the back.
Referee Mike Dean allowed play to continue with Michu lying prone inside the Spurs area as Andros Townsend almost scored a second for the hosts, with both benches arguing on the touchline.
Laudrup conceded that the challenge was a fair one but was initially worried about the way Michu had fallen to the ground.
"Fortunately he is OK," he said. "When I saw it I thought 'Oh hell, he is unconscious, you can't fake a reaction like that' - it isn't like when someone kicks you, this is completely different."
Laudrup was angry with the decision from Dean and his officials not to call a halt to proceedings to allow Michu to receive immediate medical attention and believes they should have communicated among themselves to come to the right decision.
He said: "I was very angry and it wasn't because I wasn't a free-kick or a red card for Lloris or a penalty or whatever but we always talk about people, there is a debate, should we kick the ball out.
"It is the same debate in every country - we have a referee and two linesmen so we just go on until the referee blows the whistle.
"But with possible head injuries, like this one, there is no doubt, you have all the linesmen and the referee and they are connected.
"I watched it afterward on the television and when it happened, when Michu is going down to the ground the referee is watching them, the linesman is watching them and still they let the game go on, it is such a poor decision and dangerous as well."
Swansea defender Chico reacted angrily and approached a number of Spurs players for continuing, with both home boss Andre Villas-Boas and substitute Jake Livermore running onto the pitch.
Laudrup revealed a mix-up was the cause of the reaction of the Spurs bench.
"In the beginning I think some from the Tottenham bench thought we wanted a red card or a penalty or whatever, but that is not the issue we just wanted him to stop the game," he said.
"They waited and they had a counter-attack and I said 'I don't care if they score a second goal, I just want the game to be stopped."
"I didn't (speak to the referee after the game) it will be nice to hear his explanation, and the lineman as well.
"I want referees and linesmen to do exactly the same as players and learn from their mistakes."
Villas-Boas agreed with Laudrup that the game should have been halted, and was more concerned with Michu's condition than his side wrapping up the game with a late goal.
"On the incident I was expecting the referee to stop the game immediately," he said.
"It is a difficult decision for Mike because Townsend is running through on goal, but the health of a player is more important. We were trying for the game to stop immediately and I think all of the mess came as a consequence of that.
"On that split-second he has to make a decision, but to be fair we jumped from the bench straightaway to try and stop the game."
Spurs held on for over eight minutes of added time to record a slim victory that sees them move back into the top four in the Barclays Premier League.
Villas-Boas believes his players showed desire not to concede a late equaliser, with much made of their inability to keep out late goals.
And the Portuguese revealed it was something the squad had been working on at the training ground.
"I think if there was one team to win this game it was us," he said.
"We were very patient and persistent in what we were doing and kept moving the ball well.
"We held on to the win. Obviously in this season we will continue to suffer goals in the last minute because football is unpredictable, but I think today the players showed the desire and ambition to put the wrong right and we managed to hang on to the result.
"We address it (conceding late goals) as a group in training by stimulating concentration in the last parts training. It is very difficult because you can't replicate the stress of a game and environment of a game.
"By increasing the complexity in terms of the exercises that you do, so the more complex the exercise the more concentrated you have to be, to do it you have to be very creative."