The Anfield club, who face Leicester City at home in the Premier League on Friday, paid £40 million to steal the Netherlands star from under the noses of rivals Manchester United.
The 23-year-old forward shone for his country at the World Cup, scoring three goals in the group stage.
It is believed that his national team captain Virgil van Dijk played a big role in persuading Gakpo to join him at Anfield rather than moving to Old Trafford, where United's Dutch boss Erik ten Hag is a big admirer.
But the signing means Liverpool may have less to spend on other priorities such as strengthening their midfield.
“The money you spend impacts on the money you can spend. Same for anyone,” Klopp said.
“But we know what we want to do and see if we can do it. It’s about money of course but it’s more about how it always was – the right players. We are really, really happy we got Cody.
“It’s about timing and getting players in at the right moment. He always made the next step.
“We believe in our process, when players, especially offensive ones, they all make a step forward because of the way we work and can help them.”
Liverpool are currently sixth in the Premier League, five points off a top-four place, but will look to continue their recent good form in the league when they take on Leicester.
The Reds beat Aston Villa 3-1 at Villa Park on Boxing Day on their return to action after the World Cup break. It was their third straight win in the league as they look to move up into a Champions League spot.
Klopp's side have injury problems, though, with forwards Luis Diaz, Roberto Firmino and Diogo Jota all sidelined.
Gakpo cannot play against Leicester as he can only officially sign for the club when the transfer window opens on January 1.
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Leicester also face injury issues, with midfielder James Maddison set to miss Friday's game due to a knee injury.
Maddison went off after scoring in Leicester's 2-0 win at West Ham United before the World Cup and, while he was part of England's squad in Qatar, he did not play.
"Maddison won't be available for the game," Leicester manager Brendan Rodgers said on Wednesday. "He was with (club doctor) Mark Waller getting some special advice in London so I'll wait to hear from them later on.
"He hasn't trained with the squad. He was clearly getting treatment out (in Qatar) and he and the medical team deemed him OK to train. He was available for games for England.
"He's come back, looked to do some work, and felt a pain in a different part of his knee."
Maddison had been in superb form for 13th-placed Leicester this season with seven goals and four assists in the league.
Belgian midfielder Dennis Praet will also miss the Liverpool game having suffered a knock early in Leicester's 3-0 defeat by Newcastle United on Monday after replacing Maddison in the starting line-up.