"I think we can play much better than we did as this was by no means our best performance," Bruckner told the post-match press conference.
Switzerland were obviously the better side throughout the game, but Czech claimed a precious victory to open their EURO campaign in the best possible way.
"We did a good job. Three points from the first game is a great start and a great boost for the rest of our group campaign."
Striker Vaclav Sverkos, 23, scored the winner after replacing giant striker Jan Koller in the second half.
Bruckner explained his decision to introduce the Banik Ostrava man, who repaid his coach by netting the decisive strike in the 70th minute.
"In the second half, I brought on Vaclav Sverkos for Jan Koller because we hadn't really done enough going forward and you need quicker players later in a game."
"It turned into a good substitution but I still don't think we'll win the group," Bruckner added.