"Hendo is so important to us, not only as a player but also as a person and as a leader", Klopp told the Liverpool Echo.
There had been wholesale changes - including Loris Karius replacing Alisson on the latter's maiden Anfield appearance - and two substitutes combined to make sure of victory.
The dynamic Alex Oxlade-Chamberlain, in theory, is another contender but considering he's recovering from a serious knee injury, will likely not be in action till the end of the 2018/19 season at the earliest.
"I have no clue what we will do at the weekend".
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New goalkeeper Alisson started for Liverpool, before Loris Karius was given a rousing reception when he replaced the Brazilian in the second half, just over two months after suffering concussion and making two awful errors in the Champions League final defeat by Real Madrid. "He was very comfortable on the ball five minutes in and it meant we could show for it and he was starting most of our play, so it was a very good performance from him".
Signs have been incredibly positive for Klopp who has seen the Reds on the losing side just once in eight pre-season outings this summer, the most recent of which came on Saturday, when they beat Napoli 5-0 away from home.
"Dejan (Lovren) is in but he's not had a long holiday (after the World Cup final)".
Midfielders Fabinho and Marko Grujic both filled in after Van Dijk was replaced at the break, but Klopp insists that he is not anxious about that before Liverpool welcome West Ham United to Anfield on Sunday.