The former United, Sunderland and Derby County man made his comments during the Hammers’ Premier League game against Liverpool at Anfield on Saturday afternoon.
Lanzini started the match and scored the opening goal after just three minutes, as West Ham went on to win the encounter 3-0.
Higginbotham was impressed with how the Argentine youngster, who joined the Hammers on a season-long loan deal from Al Jazira Club last month, started the game against Liverpool.
Lanzini gave a good account of himself for West Ham during the 82 minutes he was on the pitch at Anfield.
The 22-year-old attacking midfielder took three shots, had a pass accuracy of 82%, put in one cross, attempted one dribble, won 67% of the tackles, and made two blocks.