Shaqiri struck the winner in the 2-1 triumph over Serbia on matchday two, a goal that has put Switzerland within touching distance of the last 16.
The Stoke City forward has been involved in five of his country's last six goals at the World Cup and scored a hat-trick against Honduras at this stage of the 2014 finals to send his side into the knockout phase.
Switzerland coach Vladimir Petkovic applied the "organised chaos" epithet to Shaqiri's performance against Serbia, but Waston said his side must focus on its own qualities as it looks to end a disappointing campaign with a win.
"He has the potential, right?" he told a news conference when asked about Shaqiri. "We know their qualities but the most important thing is what we do.
"We've got to be sharp in our back line but in front as well. We got to create chances and hopefully get a goal, in set-pieces or whatever, but hopefully we find a way to score.
"Very often we don't prioritise little details but often those make the difference. You can never relax in a game. That always has consequences. Sometimes, playing for a club or in CONCACAF, I sometimes don't feel as exposed as I do here. Here, the level of play is so high, you have to be very careful."
Costa Rica has been heavily criticised back home for its results in Russia, with defeats to Serbia and Brazil meaning it cannot progress to the next round.
Waston, who will return to MLS duty with Vancouver Whitecaps after the match in Nizhny Novgorod, does not think the fact it is playing only for pride has reduced the pressure on his team's shoulders.
"I don't think we could be under more pressure!" he said. "We want to get a positive result. We need to score to be able to win. That's our aim: to finish our last game with a win."