Two own goals from Jonathan Walters, an Eden Hazard strike and a Lampard penalty helped Rafael Benitez's side inflict Stoke's first defeat at the Britannia Stadium this season.
But, with the Blues having suffered a 1-0 loss to relegation-threatened local rivals QPR in their last game at home, the 34-year-old is keen for his side to maintain momentum.
"At the moment we are a better away team than home team because the results speak for themselves but that has got to change against Southampton on Wednesday," Lampard told the club's official website.
"We have to start quicker and get the movement and the passing going like we did at Stoke.
"We can play different ways and we are doing it well away from home, but it is a case of sustaining things when you are attacking - following up the play and trying to play quickly on either side. It is all things we can do and I think people will see us do it now. We have to.
"I hate the idea of standards dropping and we have been up there a long time trying to win the league, or a bad year was coming second.
"The minute you drop your standards too far below then you will settle for that and there is a desire and a determination among the players and the staff, from the squad and the club to keep where we want to be."
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"You make your luck and we could have had a lot more goals. Eden Hazard's goal was fantastic but I had a couple of chances and we dominated and looked dangerous, and there was certainly no luck in the win," Lampard added.
"I was just pleased to see my penalty hit the back of the net to make the game clear. I could have gone past Kerry Dixon's total by a couple but Begovic is a very good keeper and the first-half chance he made a good save with his legs and the second-half one I am a bit frustrated about because I was close-range on my left peg and I just wanted to keep it down.
"But the main thing was the team performance. No one gets results at Stoke this year and off the back of Swansea we played fantastically."
Lampard's spot-kick marked his 194th goal for the west London outfit, helping him beyond Kerry Dixon and taking him within eight goals of the club's all-time top scorer Bobby Tambling.
"Everyone mentions it with every goal I score and it is something I would be very proud of," he added.
"But I love playing in a performance like Saturday and if I can keep doing that until the end of the season then I will be happy."