The dropped points means Arrasate's side are not yet assured of European action next season, although the sixth-placed side need just two points from their final two games to see off the late challenge of Villarreal in seventh.
Arrasate's men have two tough fixtures to close out the season, too, which could make Sociedad's profligacy on Monday all the more crucial - with their Basque derby with Athletic Bilbao followed by a last-day hosting of Villarreal in a potential European spot decider.
"It's a tough blow to take and we feel bad, because I think we've done enough things well enough to have to have won the game by a comfortable margin of goals," the coach said.
"On top of that, we're told that their goal was offside, but that's no excuse."
Arrasate said his side should have had a comfortable lead through 45 minutes but they did not convert their dominance until the 78th minute when Carlos Vela scored.
The Sociedad boss claimed the dismissals of Granada's Recio and his own defender Mikel Gonzalez three minutes apart opened up the game for more attacks.
"We had a great first half, with more chances and more dominance of the game," he said.
"In the second half though, things evened out a little and with the two dismissals, the game was broken and opened up a lot more.
"We got ourselves ahead but we weren't able to hold onto our lead."
Arrasate went on to claim his side should have finished the game with 11 men.
"Mikel didn't time his challenge well, but for me, it wasn't a red-card foul," he said.
"The referee had just sent off a Granada player, so there was always the danger of this happening."
Sociedad still remain favourites to reach the UEFA Europa League but Arrasate was disappointed not to be pushing fifth-placed Sevilla, who are two points above them.
"It's a shame because with a win, we'd have been on the right track in the fight for fifth place and have sixth place guaranteed," he said.
"Now though, this draw complicates things for us in sixth and we're two points behind fifth.
"We no longer depend on ourselves, but we've got two games to go and we'll keep fighting to finish as high as we possibly can."
