A Joel Ward own goal and two finishes from club-record signing Steve Mounié sent Town top of the Premier League on the opening Saturday of the new campaign.
However, Wagner was quick to laugh off his side's ascent to the summit after the 3-0 win at Selhurst Park.
"Let's just focus on our performance, which was good, and the result which was excellent - nobody will be looking at the table,” David Wagner said after the game.
"We should not look too far ahead, we should focus on what we have seen and that made me very happy.
“You cannot moan if you play your first game in the top flight in 45 years and you win 3-0 away.
“We know we were very clinical and had bit of luck when they missed chances.
"Our game plan of pressing them as high as possible and keeping them away from goal worked, alongside the togetherness and fighting attitude we had.
"It was a great debut for Steve Mounié and we had a great goalkeeper (Jonas Lossl) as well and that helped massively.
“Did I expect this result? No, but I hoped it could happen. This makes for a wonderful afternoon."
The 45-year-old also went on the refute claims the result sent a statement of intent to the rest of the league and pundits who have tipped his side to struggle this season.
“We don't have to send a statement to pundits, we only like to be focused on ourselves,” Wagner added.
“Pundits have to say something - this is their right and we accept it but it doesn't change how we work.
“We are still progressing and still have to improve - we are far away from our best and far from being ready.
“Now I can't wait to play our first ever home Premier League game in the club's history against Newcastle United.”