Suarez promises the best is yet to come after flying start at Anfield

Luis Suarez didn't have too much trouble filling the spaces between games in the Netherlands. Liverpool's new folk hero will be remembered in the country where he made his name as the face of a TV advertising campaign promoting discreet hearing aids.

The campaign revealed a humour that was both self-deprecatory – he was hired because of his pointy ears – and deadpan. Suarez is seen expounding hopes that a product designed to eliminate irritating background aural interference would block out the "very annoying" sounds of referees' whistles.

But Suarez didn't have too many empty hours to fill in Ajax, where he played as he pleased at the club he captained. Having swapped the canals of Amsterdam for the banks of the Mersey, he finds himself blocked out of European adventures, because his former club's drop from Champions League to Europa League – where Liverpool compete – has rendered him ineligible. That has meant plenty of weeks like this one, kicking his heels, waiting for a chance to build on what he has started. "It is very difficult for me to play one week and then have to wait two weeks for the next chance to play," Suarez said yesterday, as he reflected on his extraordinary, match-winning display against Manchester United. "I am playing one game, and then there is not another game I can play in for a long time, and so it is hard for me to get to the right level physically."

Suarez feels he has not reached his zenith yet. "Yes, I think it will take some time before the fans can see the best of me. That is what I am working towards every day, to doing my best for the fans," said a player who has been blithely unaware of the Kop's anthem for him: "I just can't seem to get enough Suarez" sung to the Depeche Mode tune. But there was something in the sangfroid he displayed at the weekend that suggested this was an individual who, as new No 7s go, was destined to be considerably more Kenny Dalglish than Robbie Keane. The only game he had ever felt pressure in, the Uruguayan said, was a Nacional v Penarol game back in Montevideo, when he was 18. "It is worse if you get obsessed with how big a game it is and get nervous three or four days before, because you take that into the game."

Suarez insists he has been blessed with luck – "When I was younger and I tried to beat a defender there and it didn't work, the ball would always end up back at my feet somehow" – though the sangfroid is the more significant quality. Keane's story attests to the problems that Anfield's weight of expectation can bring, though Suarez seems above all that. His debut goal from the bench after 13 minutes against Stoke City had an element of that lucky quality about it, but the decisive spin and cross at West Ham suggested that Suarez was ready to deliver instantly. The seven-game ban he had just concluded when he left Ajax seems, if anything, to have sharpened his senses.

"His influence since he arrived here is really good. He scored in his first game, he was very close to scoring against Wigan and he created a goal against West Ham for Glen Johnson," recognised Dirk Kuyt yesterday, two of the three goals he scored on Sunday having been provided by the Uruguayan. "For him to be at his best after just a couple of weeks at the club is impossible but he has shown the will to be a great player for Liverpool."

The most exciting aspect for Liverpool fans is that the partnership of Suarez and Andy Carroll has barely been tried out and even the customarily sanguine Dalglish could not disguise his anticipation. "I don't ever make a library of players' performances but I know Luis is a fantastic footballer and is still trying to find his feet here," said the manager. "I am really looking forward to him and Andy forming a partnership."

Dalglish the pragmatist deliberately resurrected the memory of the previous week's performance. "You can never take away the disappointment of West Ham. We can use that as a reference point," he said. But that image of his beaming face as Suarez was substituted told the true story. With Suarez starting like this, Dalglish now believes that a Champions League place is not beyond his side.