Michu signed for the Swans from Rayo Vallecano for a £2 million fee, and it was only last week that Laudrup was adamant his new acquisition would show his worth in this league despite the relatively low outlay.
Now the former Real Madrid and Barcelona man wants his attacking midfielder to show Swans fans that there is no need to worry after the failure to secure Gylfi Sigurdsson's permanent signature.
The Dane told reporters: "He gives us a lot. When we have the ball he is a second striker; when the opposition have the ball he is the third midfielder. It’s a very important position for us.
“Sometimes, for 15 or 20 minutes in the first half at Queens Park Rangers, we got a little too deep and Michu was too far from Danny [Graham].
“We had some problems at the start but every day Michu is getting better and he will get better from now.”
Swansea's new boss reportedly informed the club's officials of how exciting the Spaniard would prove to be for the Swans and exploited Rayo's difficult financial situation in Spain to seal Michu's signature.
After witnessing them first-hand in destroying Mark Hughes' men at the weekend, Laudrup feels his new boys will easily adapt to the Premier League.
“You can get a lot of quality for a reasonable amount in Spain right now, he said.
"We are talking about players who have played at the highest level. There are some small differences in style between the Premier League and La Liga, but they are the two best leagues in the world.
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“All three players have the experience of playing at the level. We defended a little too deep in the first half, but Chico did well alongside Ashley [Williams].
“And Jonathan [de Guzman] did well for 65 minutes before he came off.
“He had a difficult year last year, playing for a team who normally fight for Champions League places but ended up getting relegated.
“But I know him. I know that in some weeks, he will get the last 15 or 20 per cent that he needs and in a month’s time he could give us 90 minutes, no problem.”