The Dane, who took over at the Liberty Stadium in 2012, has seen his side fail to win in their last eight Premier League matches.
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Asked after the loss to Tim Sherwood's team whether it was his toughest time at Swansea, Laudrup told reporters: "Yeah, yeah of course it is."
However, Laudrup remains confident the club will come out of their current troubles stronger, having risen from League Two in 2005 to the Premier League in just six years before winning the Capital One Cup last season.
"This is a club and a team used to things going well, more or less, and I said it the other day - when you're at the highest level you need to suffer sometimes," he added.
"Until now, I think in the last years Swansea hadn't had difficult moments overall. Even if it's negative now, I think it's a positive.
"I think it will be positive after because when you come out after you have been struggling, whatever team you are, you appreciate it more - what you have done and what you have.
"Maybe some could think that, being a mid-table team, without ever having to worry about relegation, that [relegation] would just be for the others.
"We can't think about it like that. Clubs with many years in the Premier League struggle so it's good - even if it's not so nice now."