The 41-year-old took over as boss on July 4 after leaving Derby County.
Azpilicueta has revealed the impact Lampard has had already on his players.
"It is true that last season, for periods, we didn't give the fans what they expected," Azpilicueta said. "Our performances were not good enough.
"We turned it around and won the Europa League but you can see that this season all of the fans are very happy we have the gaffer back at the Bridge.
"Now we have to give it back by working hard on the pitch, by winning games. We are very happy to have him with us. I can't add anything to his career at Chelsea as a player.
"But, over his first week in training, I've seen the way he wants to play, the way he wants us to feel the shirt, the way he wants us to train every day, it is something special."