The Brazil midfielder was pressed into service as an emergency central defender at the Amex Stadium, but produced an assured display as the Reds prevailed 1-0.
Asked if Fabinho could play in defence again if needed, Klopp replied: “He is a brilliant player and I am happy that he can play (against Brighton) – it’s now pretty clear (that he can play in defence).
“It’s not like it came one attack after the other from Brighton. We had the ball most of the time, so then it makes sense to have a good footballer in that position.
“I think Brighton tried a little bit to bring the long balls and (Glenn) Murray around him. That’s what they did, by the way, against Joe Gomez in the home game as well.
“He did well in these situations and with the ball it’s absolutely clear. He has a defending brain and can do it in different positions, it’s good.”
England full-back Trent Alexander-Arnold suffered an injury scare in the warm-up at Brighton, stepping on the ball.
Klopp confirmed the 20-year-old picked up an ankle concern, but he remains hopeful he will not to lose the talented right-back for any future fixtures.
“The last situation warming up, I think he stepped on the ball, I didn’t see the situation, I only saw him going down,” said Klopp.
“Trent on the ground – he’s a hard boy so that’s not a good sign and the doc came, something with the ankle.
“And it was pretty painful. He made the sprints, but I didn’t like the way he did the sprints because when he slowed down, I thought it looked a bit like limping.
“In the dressing room, he told me the pain is away, then doc made a little treatment, made a strapping, go out.
“I don’t know exactly what it was and I hope it will not take long, that he doesn’t feel it any more.”