Uruguay were expected to claim all three points in the opening game of Group D, but Arsenal striker Campbell insisted that the win was no surprise for him and his teammates.
"It wasn't a surprise for us," Campbell told FIFA.com. "We came here to win. We wanted the points and we went for them.
"Despite the fact that they were winning 1-0 we stayed positive. We knew that we were going to win.
"We never thought about losing and thank God we got the result."
Costa Rica will be hoping to maintain their form for the game against Italy on Friday.