Lampard marked his 500th Premier League start with his sides fourth, his 130th Chelsea goal in the Premier League, taking him past the previous mark set by Bobby Tambling.
However, the midfielder, 34, is out of contract at the end of this season and has so far not received the offer of a new deal from the club.
“I’m not concentrating that far as I’m under contract and I love playing here so I’m going to continue game by game and just be pleased to be fit. I really enjoyed this match and just want to keep enjoying my football. I believe I have a lot in me to go,” he said.
“The club’s position is its position, I don’t want to get too deep into that. I’m here to play football and show people what I can do and I’ll continue to do that,” he added.
He added: “The record means a lot. The starts are great, I’ve been very fortunate to play for a great club and the managers and team-mates I’ve had, I’m very proud of that. The goals record, I’m very proud to beat such a great man as Bobby Tambling, who is an absolute legend and a lovely bloke.”
The Chelsea goals were shared between seven players with Fernando Torres, David Luiz, Branislav Ivanovic, Oscar, Ramires (2) and Eden Hazard also on target while Lucas Piazon missed a penalty.
Chelsea interim manager Rafael Benitez said after the game that he still believes his side are still in the title race after moving back to third, 11 points behind leaders Manchester United. He said, “The main thing is to win our games. You can do that if you can see the team improving. I’m sure it will be closer.”
Meanwhile, Benitez confirmed that striker Daniel Sturridge has undergone a medical at Liverpool and is expected to leave Chelsea when the January transfer window opens.