Lampard netted the fifth goal of the afternoon to become the club's joint second highest scorer of all time and looked particularly emotional during his celebrations.
"They supported me throughout my career here and particularly in recent weeks," he said of the Chelsea fans.
"The way they were with me then is the way they have been recently and all the time I've been here. I just wanted to say thanks back.
"That is our platform to say thanks back when we're on the pitch, to first of all do the business because they pay the money to come and watch and when they have been so good to me, just to say it back to them. That is genuinely how I feel.
"This club has been amazing to me and the club is the fans so I can only thank them.
"I am enjoying my football, I have to say. I am enjoying the moment.
"I know there is a lot of talking going around but I am actually really enjoying playing.
"That's what it is all about really so even if there is certain things going on your head, I think when I run out there and the fans support me the way I do, it can't help but make you a bit emotional."