Alcaraz's men bravely equalised in the 93rd minute through Odion Ighalo, although at the suggestion the goal should have been flagged for offside from a journalist in the post-match press conference, the Granada boss let rip into referee Fernando Teixeira.
"Who are you, a linesman? What about the penalty for (Diego) Buonanotte?" Alcaraz said.
"What about the dismissal of Recio and the penalty that provoked that? Did you see that? Anything else you want to discuss?
"What about the added time, when the fourth official showed three minutes and we played five more?
"They had the last free-kick, there was a clearance, we were counter-attacking and the referee blew for time.
"Anything else I've missed? I think we're best leaving it there."
Alcaraz, though, hailed his side's fight at the Estadio Municipal de Anoeta, with the point taking them three clear of the drop zone with two games to play.
The Granada boss claimed Sociedad had already sewed up their European spot, despite their opponents only five points clear of seventh-placed Villarreal.
"There are stadiums where it always seems you're going to lose and others where you can see yourself getting points, just as happened today and last season (2-2 draw) here at Anoeta," Alcaraz said.
"We've competed well against an opponent who had their objective already achieved, but they (Sociedad) haven't dropped their level, which is something that isn't happening at many other places.
"In this sense, we've shown that we came here, we wanted a result and we've overcome going a goal behind. It was tough at the start, but the game was much more even later on."
Real Sociedad remain in pole position to sew up a UEFA Europa League spot despite dropping points at home.
Alcaraz said his side's 3-0 loss at home to Rayo Vallecano in late April had spurred his side into action, with Ighalo's goal their first in 347 minutes since their famous 1-0 win over Barcelona.
"The team came into this game hurting about our result against Rayo," he said.
"My players showed a lot of faith and with determination, they were able to compete and draw a game that could have been won just as easily as it could have been lost."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.