"In France we went into our last game really wanting something even though we were out.
"From that experience maybe we can learn that they will really be wanting to give the Polish people something to be proud of.
"We have to go into that game and be prepared and respect them," said Reyna.
Although the US are playing in their fourth successive World Cup, success has been lacking.
Before their match against Portugal, they had managed just one win in 10 matches dating back to Italy 1990, with five of their eight losses in succession.
America's best performance was a second round appearance, and subsequent defeat by Brazil, at USA 1994.
A berth in the second round in 2002 would not only equal America's performance of eight years ago, but also help ease the bitter memories of France 1998 that saw the US finish last in the 32 nation field.