The Swans manager felt his side were perhaps better value for at least a draw at White Hart Lane, despite their lack of attempts on goal.
"I think we did well for the first 30 minutes and last 10 minutes. We created a couple of chances," Laudrup told Sky Sports.
"Lloris made an excellent save from Chico too."
Laudrup, who saw Roberto Soldado coolly sweep home the spot-kick after Jonjo Shelvey was adjudged to have felled Andros Townsend, felt aggrieved by Neil Swarbrick's game-changing decision to point to the spot.
"They won a light penalty in my opinion.
"We were punished by that penalty in the second half. It was the only time they really created something."
Despite two losses from the opening two games, the Dane was keen to play down any possible panic for the Welsh side.
"We knew already when we saw the fixtures, playing the champions and Tottenham away it'd be difficult.
"We know this competition is very long. Six points in two games last year but after seven games we had eight points. We'll see where we are at that stage this season.
"There's a lot of games. It's no problem and we want to get some points now."
Speaking on signings, Laudrup feels that his side are possibly lacking a striker, but isn't rushing into the market just yet with the deadline looming.
"We're looking for maybe one more forward with different qualities, but there's still some way to go."