The defensive midfielder has been absent for recent games, but he made his return during the 2-2 draw with Shrewsbury Town in the FA Cup last weekend.
Fabinho is still improving his fitness, and Klopp hopes he can take another step forward in the coming games.
Klopp also spoke about how he could easily reshuffle his midfield to accommodate the Brazilian.
"It was easy to move Hendo. Fabinho is naturally more a defensive-orientated player than Hendo," Klopp told reporters.
"We had to control the counter-attacks of Southampton. He [Fabinho] has struggled with rhythm. The first two games when he came on it was not Fabinho before he got injured. That is normal, so Saturday was a big step for him. He was key for us.
"We needed a calm player in the centre, not too active. That was the change at half-time. We used him more for the switches - find Fabinho, pass to the other side and then accelerate and use the power of Hendo in the half-spaces."