Gunnarsson notched the home team's opener as the Bluebirds beat Manuel Pellegrini's side 3-2 to record their first-ever Premier League win.
And the Icelandic international believes there is more to come from Malky Mackay's side as they bid to establish themselves in the top flight.
He told the Daily Express: "We did really well and other clubs will be watching that.
"We're hard to beat and we work hard for each other - that's what this club is about.
"It's a massive three points. No one thought we could do it but we're off the mark and will carry on.
"We believe in ourselves and have to continue to do that if we are to do something in this league.
"It takes the pressure off us."
Gunnarsson feels Cardiff's set-piece play could prove pivotal in their campaign, saying: "We were strong at set-pieces last year - about 51 per cent of our goals came from there."