Randall Alvarado's 12th-minute goal would be enough for Wright's men to take all three points from their trip to the Estadio Jose Rafael Fello Meza on Sunday.
Cartagines sit second in the standings - two points behind leaders UCR - but have a game in hand.
Wright, however, said his side "had two clear chances, incredibly we could not finish them".
However, the former Costa Rica international hailed goalkeeper Alejandro Gomez, who kept his first clean sheet this season in his second start.
With custodians Luis Torres (hernia) and Wardy Alfaro unavailable, Wright said he was "blessed" to have the services of 25-year-old Gomez in goal.
Cartagines snapped a run of two draws to take all three points, and keep the pressure on UCR, who were 3-0 winners at Carmelita on Monday.
Ariel Contreras, Allan Duarte and Victor Coto were all on the scoresheet for Jose Antonio Giacone's men.
Santos de Guapiles salvaged a 2-2 draw at home to Perez Zeledon, after coughing up a lead.
The hosts led when Javier Loaiza netted in the 49th minute, but were bound for defeat when Alejandro Alpizar and Fabrizio Ronchetti scored 13 minutes apart.
However, Antonio Salazar's goal with three regulation minutes remaining earned a point for Santos, who sit fifth in the table with 10 points - goal difference behind third-placed Deportivo Saprissa.
Uruguay celebrated their first win of the season, downing 10-man Belen Siglo XXI 1-0.
Ulises Segura scored what would be the winner for Uruguay in the 44th minute, before the visitors had Ariel Santana sent off just past the hour-mark.
