Lampard had deemed Zappacosta surplus to requirement this season at Stamford Bridge.
Zappacosta joined AS Roma on a season-long loan from Chelsea.
“I spoke to Emerson and Rudiger,” Zappacosta was quoted by Insidefutbol as telling reporters at a press conference on Thursday.
“They said that the supporters will push you and I would enjoy being in the group.
“And what they told me, I have immediately found to be true.”
He added: “I was lucky enough to win the Europa League and of course we aim to do our best in every competition.
“We will do our best to achieve as much as possible.”