Pappa was released by Heerenveen and entered the MLS Allocation process, being selected by the Seattle Sounders FC who had the first pick. He was officially given the number 10 jersey last worn by Mauro Rosales on 12 February 2014. On 25 October, Pappa came off the bench and scored twice as the Sounders defeated the Los Angeles Galaxy 2−0 to clinch the Supporters' Shield, as the best club in MLS during the regular season.
During 2014 World Cup qualification, he scored the first goal of a 4–0 win against Saint Vincent and the Grenadines during the 2nd round, and in the third round, he scored from a direct free kick to equalize 1–1 at home against the United States.
At the 2014 Copa Centroamericana, Pappa helped Guatemala to a runner-up finish and qualification for the 2015 CONCACAF Gold Cup. He scored four goals in four matches en route to winning the tournament's Golden Boot as its top scorer and the Golden Ball as its best player.