He then went on to play for FC United (Massachusetts) and FC Greater Boston Bolts, before joining the New England Revolution academy team in 2009. He was a State Cup finalist with FC United 2005 and winner in 2006. He won the State Cup with FC Greater Boston Bolts in 2008 and 2009. He also played for the Massachusetts Olympic Development Program (ODP) from 2006 to 2009, as captain from 2008 to 2009. He was named a 2007–2008 Adidas Interregional All-Star as a member of the Region I ODP team. In his debut season he led the Revs’ U-16 squad to a 14–7–8 record (50 pts), placing first in the Northeast Division of the US Soccer Development Academy. He scored 20 goals in 30 appearances, tying Felix Debona for the team lead in goals.

On November 15, 2010, Fagúndez was signed to a contract by the New England Revolution, making him the first ever homegrown player the Revolution signed from its youth academy. Although on the main club roster, he continued to train with and play for the academy team.

On March 10, 2011, Top Drawer Soccer named Fagúndez their number one ranked player nationally in the class of 2013.

He made his full professional debut on April 26, 2011, in a Revs’ 3–2 victory over D.C. United in the Lamar Hunt US Open Cup. He made his league debut on August 6, 2011, as a substitute against Chivas USA, where he drew a penalty (which was converted by Shalrie Joseph) and scored his first goal for New England.

Fagúndez is a former Uruguay youth international. He made his debut for Uruguay U20 team in October 2012. He played two games for Uruguay U20 against Peru in that month. In the first he entered as a substitute in the 83rd minute; in the second fixture he was brought on in the 45th minute.

Fagúndez became a regular starter for the New England Revolution in 2013, when he had a successful breakout season, scoring 13 goals and assisting 7. Fagúndez quickly became one of MLS’s great young talents, and won player of the week honors in week 14 of the 2013 MLS season. Fagúndez obtained a US green card in October 2013 qualifying him as a domestic player under MLS squad rules. He was featured on an episode of documentary television show that MLS 36 in August 2013. During the 2015 season, Fagúndez became the youngest player in MLS history to reach 100 appearances for his club.

In April 2013, he stated that he would be willing to represent either Uruguay or the United States at the 2013 FIFA U-20 World Cup. However, he was not called up by Uruguay and was not eligible for represent U.S. at the time due to not having citizenship.

Fagúndez received his U.S. green card in October 2013, which qualifies him as a domestic player for MLS roster purposes.

In August 2014, he was called up again for the Uruguay U20 national team and played in two games against Peru, a 1–0 win victory and a 1–1 draw.

In January 2015, Fagúndez was called up for the 2015 South American Youth Championship. He played in Uruguay’s 1–0 victory over Colombia.

On October 28, 2018, prior to the Revolution’s final match of the 2018 season, Diego’s father (who also serves as Diego’s agent) posted a tweet insinuating that it could be his son’s final appearance for the franchise. The match, against the Montreal Impact, saw Diego’s 50th career MLS goal. He is currently the youngest player in MLS history to score 50 goals.

On January 22, 2019, multiple sources reported that the Revolution turned down an offer from Club Nacional de Football for Diego.