Goals at the start of each half from Michu and Nathan Dyer were enough to sink a poor Palace side 2-0.
Laudrup said: "We were the better team from the first to the last minute. Scoring a goal in the first minute of each half helps but we we controlled the game completely, scored two goals and could have scored three or four.
"It was a great performance and maybe we should have scored more. But it's an away win on the back of two very difficult games. It is three points and another clean sheet and I'm very pleased.
"When I saw the fixture for this week I said the Crystal Palace fixture would be the most difficult because of the the schedule. They need their points at home and I expected a difficult game, but it was a very good performance and it has been a great week."
Laudrup rang the changes again on Sunday, as he did on Thursday in their Europa League win at Valencia, and said he was happy with the squad he has assembled.
Laudrup added: "We are trying to use the squad. I made for four or five changes on Thursday and I did the same today, but I need everyone. You cannot play with the same 11 every week.
"This year we have a very good squad and I have to use them because we have a couple of injuries, but we can handle that.
"The new signings have adapted well and I am pleased but you have to get results and we have had a very difficult start to the season."
After starring for Swansea last season, Sunday's man-of-the-match Michu has started comparatively slowly - until this week, that is, as he capped another fine display with a goal.
"I don't know if he is back to his best, because what is his best?" Laudrup asked.
"I don't look at him as just a goalscorer because for me he is not even a centre-forward. He has always been an offensive midfielder than can score goals, but can also play as a centre-forward.
"I don't look at Michu just as a goalscorer so I don't see it as a problem when he does not score for three games."
Michu's form last season saw him rewarded with a new and improved four-year deal in January, just six months after moving to the Liberty Stadium.
Despite that, speculation was rife over the summer that a bigger club could swoop for the Spaniard - not that Laudrup was ever worried.
"What is so important when you talk about interest from other clubs, the most important thing is what the player wants," he said.
"I know you have a contract and all that, but it is important what the player wants and then secondly what the club says.
"There have been some cases during the summer at other clubs, but Michu wants to stay.
"He wants to stay after his first season because he wanted to participate in the second year, with Europe and with everything.
"What happens in the future, next year? I don't know. But I think it is so important what the player wants and I don't think Michu had any doubts that he wanted to stay here this season."