Lampard paid tribute to the man he replaced as Chelsea record goalscorer, before dedicating the landmark to his late mother.
"It means everything to me. It's amazing, the support I've had from team-mates, and you could see that at the end," he told Sky Sports.
"I'm thankful to each one of them as they are the ones that put it on a plate for me sometimes, and the fans have been willing me to do it for a long time and are probably frustrated alongside me not getting there.
"But I'm just delighted the way the fans were at the end. That is what means everything to me.
"Bobby Tambling is a great man, he hasn't been well recently but he's a great man and I didn't want to overcook the celebration out of respect for him. To go and break it, I was delighted and very pleased to do it today.
"I've been here a long time. I lost my Mum a few years ago and she was my biggest support."