The Dutchman, who traded Bayern Munich for Anfield last summer, has made a blistering start in the Premier League this season.
He has put in a string of dominant performances at the base of new boss Arne Slot's midfield and has played the full 90 minutes in each of the first three games.
The 22-year-oldcontinued his excellent start to the campaign in Sunday's ruthless victory over bitter rivals United, making crucial defensive interventions while pushing the side forward with pinpoint passing.
But his national manager's comments served to burst Gravenberch's bubble, with Koeman drawing attention to the weaker aspects of his game ahead of home fixtures against Bosnia and Herzegovina and Germany.
Koeman (pictured) said: 'I believed he lacked focus, this is something that he had to improve'
The former Everton and Southampton boss responded to one journalist's glowing praise for the defensive midfielder by saying: 'I am glad you added that last part. I have always seen the potential in him.
'But I believed he lacked focus, this is something that he had to improve and now it seems that he finally realises what is asked of him.'
Despite turning out 26 times for the Reds last season, Gravenberch did not play a single minute in a Euro 2024 campaign which saw the Netherlands reach the semi-finals.
The midfielder's lack of 'focus' has clearly been a sticking point for Koeman with the talent playing just 86 minutes under the manager since he assumed the role in January 2023.
Last month Slot told Gravenberch to ready himself to feature in two different positions this season.
The 22-year-old played predominantly as a box-to-box midfielder under former boss Jurgen Klopp last season following his arrival from Bayern.
While Slot has suggested that he will continue to deploy Gravenberch as a No 8 at times, he also wants to be able to use him in more of a holding role - like he did in the 2-0 win at Ipswich on the opening weekend.
Gravenberch told Liverpoolfc.com on August 24: 'I had a little chat with him (Slot) and he said I have to focus on the No 6 and No 8 positions.
'Now I play at No 6. In the past I played it as well so I know what I have to do. I've enjoyed playing there.'
Gravenberch added: 'It's a little bit of a different system than we played last season, but I think everyone has adapted to it. Now we have to build it further and further.