Vardy struck twice for the 3-0 shock.
He said, "We thought we wanted to get out after starting slow last week and we did that today.
"I think the intensity he has us playing at, we're winning the ball much higher up and we have opportunities in behind."
On fellow goalscorer Youri Tielemans, he added: "The fans are saying it, sign him up, he's been fantastic."
On his second goal from Kasper Schmeichel's kick, Vardy also said: "It's actually something we worked on in training this week, we thought Arsenal's defence would play a high line and there'd be opportunities over the top.
"We look forward to Man city next week and look to get as many points as possible."
Meanwhile, Tielemans said: "I think it's a big win today. We scored three at home against a big team and it's always a pleasure.
"It's the first header of my career. We played the full game, both halves, at high intensity and with good quality."