The 25-year-old scored what proved to be the winning goal as the Welsh outfit held out the Spanish side with a 2-1 win in a friendly at the Cardiff City Stadium on Saturday.
"We knew how good Athletic Bilbao were as a side," Campbell said in a press conference. "It's a good win. Our understanding is getting better and better the more we play.
"It'll be a tough Premier League season, but if we work hard and stick together I'm sure it'll bring results we deserve."
Peter Whittingham scored the other goal in the win.