Roberto, who has featured more often at right-back than his preferred central midfield role under Ernesto Valverde, hobbled off at half-time in Athens, whilst Portuguese international Gomes only featured for the final 15 minutes.
"The midfielder from Reus (Roberto) has a torn right hamstring which will keep him out for approximately five weeks," Barca said in a statement.
"(Gomes) with an injury in his right hamstring will be sidelined for around three to four weeks."
Both players will miss league games against Sevilla and Leganes, as well as a Champions League trip to Juventus.
However, Gomes could be in contention to face his old club Valencia in a top of the table La Liga clash on November 25 or 26.
Despite drawing a blank in a Champions League group game for the first time in five years, Barca remain well on course to reach the last 16 as they hold a three-point lead over Juventus with a point in Turin enough to also guarantee top spot in Group D.