Lanzini returned to the Hammers’ team in their match against Southampton, but the Argentine’s performance was overshadowed by two of his teammates.
Goals from Antonio and Carroll gave West Ham the points against Ronald Koeman’s side, and Lanzini was delighted for the attacking pair.
“It was a bit of a strange goal but he [Michail] deserved it,” the 22-year-old said. “After the equaliser he gave us power and the will to keep going forward.
“I’m very happy for the second goal because Andy means a lot to this club.”
West Ham had fallen behind in the first half of their match against Southampton, but they responded to the set back well.
Antonio drew them level, and they never looked back after that strike - with Carroll grabbing the winner.
It is the first time that West Ham have scored more than one goal in a match for their last six outings - which highlights Lanzini’s importance to the team.
The Argentine is one of the main architects for Slaven Bilic’s men, and the Hammers have struggled in his absence.
West Ham’s win over Southampton has pushed them up to eighth in the Premier League table.