Chances were at a premium for both sides with the in-form Michu going closest to scoring for the visitors when forcing Tim Howard to tip his lob onto his crossbar and out for a corner in the first half.
Laudrup said: "I'm obviously delighted to get the point after getting the win the other day at Stamford Bridge. We knew already Goodison Park is always a difficult place to go and play and to come in the same week as playing Arsenal and Chelsea was hard.
"We all know how Everton play. They are able to put everyone under pressure so it was great to get a point. We had to come here and play a different way, a way we're not used to and to get a point at a really difficult ground was excellent.
"It's been a busy time for us, we played well in midweek at Chelsea, it was similar to the Chelsea game in that we didn't play as much as we would have liked but the players adapted well against two big, physical teams and we got a good result the other day and, again, here, it was another good result.
"When games are coming so fast, you have to use much more of your squad, make two, three, four even five changes and I have a good team who adapt and play well. They still feel part of the team and I think that is very important and you can see that in past two games.
"We had one or two chances no more, we knew how it would be. You have to accept it sometimes what type of game it will be and I think the players adapted to the pressure of Everton, but they play direct, they're a big team but my defence did well."
Spain coach Vicent del Bosque was at Goodison Park, to check out the form of Swansea's top scorer Michu, but Laudrup admitted that he would probably have left with more questions than answers.
He added: "It wouldn't have been the best game to see Michu in. I know Del Bosque has other people who can tell him what sort of form he's in. They see a lot of the Premier League in Spain.
"Obviously I hope Michu has a chance to play with the best team in world at this time. The other Spanish players here also did well in front of him with Angel Rangel and Chico both having really good games."