Tottenham began its preseason North America tour facing former striker Clint Dempsey and his new club. Dempsey left Tottenham to sign with the Sounders last August.
Pochettino left Southampton in May to replace Tim Sherwood, who was fired on May 13 after just five months on the job following Tottenham's sixth-place league finish.
Alonso's goal off a loose ball zipped past Friedel and hit the underside of the crossbar before bouncing in the net. The goal gave Seattle a 2-1 lead, but Roberto Soldado converted a penalty kick in the 55th after he was fouled in the penalty area.