Hammers manager Sam Allardyce accused the Spanish defender of 'over-exaggerating' the impact of Carroll's contact, but Laudrup appeared to stick up for his player when asked if Chico had made too much of it.
The Dane told reporters: "I can't really say, maybe he did. But the referee is a very good one and must have seen the elbow that Carroll gave and judging he did that on purpose.
"If I understand the rules, it does not matter how bad it is, if there is intention it is enough. It is the same with a tackle, even if you don't catch a player it can still be a red card."
Swansea City are currently in 14th place in the Premier League table.