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 rival 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.
The midfielder went on to say that staying accountable to a certain standard was what the club really needs at this point.
|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," he said. "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."