There are once again question marks over Sturridge’s fitness ahead of next week’s Premier League opener at Arsenal after the England striker was missing from the starting line-up at Wembley through injury.
And manager Klopp was dealt another blow when Milner, who was playing in Liverpool’s problem left-back position, limped off moments before half-time.
Liverpool explained Sturridge’s absence was down to a “minor hip injury”, but Klopp conceded Milner was a major worry.
“It is not too good, it’s something to do with his heel,” said the Reds boss. “He will have a scan and then we will know more.”
Despite the injuries, Klopp could not help but be pleased following the win over the LaLiga giants.
Sadio Mane, Divock Origi and Marko Grujic all got on the scoresheet for the Reds – with a Javier Mascherano own goal the other strike – and the German admitted he has learnt more about his team from the impressive performance.
“Of course I am happy with the result,” added Klopp.
“The game was good to learn a lot of things about us. If we’d have lost, life would have gone on. It’s a friendly.
“But it was Barca and lots can happen if they start playing. When you win 4-0 you have to use it.”