The Reds put the League One outfit to the sword in convincing fashion, two different XIs putting five goals past them with Grujic scoring the first in an eight-minute spell that also saw him win a penalty and hit the post.
Jürgen Klopp was withdrawn in his praise for Grujic after full-time, despite acknowledging how well the Serbian midfielder did on his first appearance.
The Reds' No.16, who joined from Red Star Belgrade back in January, has been considered one of Europe's brightest midfield talents and Krawietz believes he has all the qualities to be a regular starter for the club in the years to come.
Backroom staff hoping for big things from Grujic
"We are very, very optimistic," Klopp's long-serving assistant Krawietz said, when quizzed about Grujic's potential. He added that they have been excited about the player "not [only] since Wednesday" because they "knew him before" but recognised his "good start."
The German insisted that Grujic is at the stage of his development where the club's backroom staff "can start to work with him" and "develop improvement with him."
Continuing to rave about the 20-year-old's talents, Krawietz told Liverpoolfc.com that Grujic "has the possibility to play in different positions in midfield" but warned that he is still "a young player" who "still has to adapt to the Premier League" and the club's "style of play."
The 44-year-old acknowledged that the squad needs a mixture of "strong players" and "tall players" for the English top-flight, insisting that Grujic "has every possibility to adapt quickly."
Reds "very happy" to have 'keeper Karius at the club
Krawietz, who recently penned a new six-year contract alongside Klopp and fellow assistant Zeljko Buvac, also praised another summer signing in goalkeeper Loris Karius.
Signed from Bundesliga side Mainz, the 23-year-old made his second warm-up appearance in featuring for 45 minutes against Fleetwood and earned another clean sheet.
The German shotstopper, who turned down the chance to represent his country at the Olympic Games in Rio next month to focus on establishing himself as No.1 at Anfield, was lauded for his efforts by Krawietz.
"This is a good sign for the club and for us," he said, on the 'keeper's promising start on Merseyside. "And a good sign for him that he is really ready to work and identify with the club."
Karius' commitment "to try to improve" and to "adapt quickly to our style of play" was also lauded by Krawietz, who suggested he has "all of things that you need in England as a goalkeeper."
He revealed that Klopp and his backroom staff are "very happy" to have Karius on board and "very happy" to have him "in pre-season to work with him."