England striker Sturridge started in the league for the first time since October after a series of injury setbacks and scored the opening goal in Liverpool's rout of Villa on Sunday.
Now Klopp hopes for an injury-free run for the 26-year-old, whose all-round game impressed his manager more than his headed goal in the 16th minute.
“Of course we need the goals of Daniel and he needs the goals, that's clear,” said Klopp.
“It's not a surprise that he scores goals, but it surprised me how good he is with the team and his movement. He is a real striker.
“It is good to see him fit and when he hides himself on the pitch he is really difficult to defend against because he is always somewhere and you don't know his next move.
“For us this is very important and changes a lot of things of course, but we can only speak about this when he is available.
“When he's not we cannot say, 'But with Daniel it would have been different.' In this game it was brilliant.”
Sturridge returned to the scoresheet on the same day that his England team-mate Danny Welbeck made his comeback for Arsenal and scored the winner against Leicester City.
Both men are eyeing a place in England's squad for Euro 2016 in France.
“It's great,” said Sturridge. “'Welbz' is a good friend of mine and he's feeling good. I spoke to him the other day and it's good to see him back.
“Hopefully we will be there in the summer and we can help the country have some success.”
For Liverpool, victory marked the end of a five-game winless run, ending a difficult period for Klopp, who saw Sturridge and Philippe Coutinho make a difference on their returns from injury.
“It is good for us when we have all our players available, but football and life is not like this,” said the German.
“You have to get results when your best players are not all available and that is what we didn't do often enough.
“We know about the problems we had and I know you (the media) are not always interested in this and that is OK.
“We believe in our work and in the squad and in the way we work and this time we got the benefit.”
James Milner, Emre Can, Divock Origi, Nathaniel Clyne and Kolo Toure also scored as Liverpool strolled to a victory that lifted them up to eighth, three points shy of the European places.
It was Villa's worst defeat at home since 1935 and plunged the Premier League's bottom club into deeper crisis.
They are now eight points adrift of safety at the foot of the table with 12 games to go and thousands of supporters walked out with less than an hour on the clock.
Many of those that remained chanted against owner Randy Lerner, while some in the main stand shouted directly at chief executive Tom Fox.
Manager Remi Garde said: “It's very disappointing. I feel humiliation.
“It was very painful with six goals conceded, but it is three points thrown away, not more. We don't have time to moan too much about this.
“It's the worst defeat I've had as a manager and I have a lot of feelings, but I will keep some of them to myself.
“As a manager it was the worst performance I've had. It was a very bad defeat. I'm very sad and frustrated. I'm very sorry for the fans.” – AFP
Original source: Klopp ‘surprised’ by Sturridge