The veteran English midfielder started in City's first-ever New York derby win over the Red Bulls which ended in a 2-0 result at Yankee Stadium on Sunday.
NYCFC's home record this season now stands at 3 win, 5 draws and 3 losses and former Chelsea star Lampard wants that ledger to start moving towards the positive if the team wants to remain at the top of the Eastern Conference table.
"You can't challenge to win things without being good at home," Lampard said.
"The more you lose at home, the more teams come in here with confidence … [to] beat you again.
"We've put a bit of a marker down now with two wins, particularly against a good Red Bulls team here."
Of the performance, Lampard added: "We had the bit between our teeth today.
"We wanted to win. They enjoyed their win here, possibly too much after the last game in the dressing room. We answered that today."