Brendan Rodgers swooped to sign the Spaniard from Celta Vigo during the close-season amid interest from the likes of Valencia.
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Aspas has made a solid start to life at Anfield, starting all three of Liverpool's Premier League fixtures as the Merseyside club have picked up 1-0 victories over Stoke City, Aston Villa and Manchester United.
And Swansea boss Laudrup has admitted that the 26-year-old is a player he wanted to bring to the Liberty Stadium, but said the lure of Liverpool was too much for Aspas to resist.
"Liverpool is a huge club, so I can't really blame him," the Dane told the South Wales Evening Post.
"I have been in football too many years to have thought we'd got him before he had signed. But yes, he was one of the players we looked at, and in the end Liverpool came in.
"He is fast, he is a goalscorer, he has good football intelligence, good movement and he is two-footed, so I think he will do well there."
Laudrup compensated for missing out on Aspas by landing Vitesse striker Wilfried Bony for a club-record fee - and revealed the Ivory Coast international would have been out of reach had they spent on the Spaniard.
"If we had got him he would have been the only one (rather than as well as Bony) because of the money involved," he added.