Carlos Vela and Juanmi, formerly of Arsenal and Southampton respectively, scored the hosts' goals as Granada suffered a fourth successive defeat under Adams.
"We are all sad, the players, the fans, everybody," said Adams.
"There's been a lot of mistakes. We're going to try to rectify it and rebound very quickly."
The 50-year-old, who took charge on 10 April, has a contract to the end of the current campaign.
However Adams has been working at the Spanish club since November and is vice president of the company owned by Granada's club president.
"If the team played like this at the beginning of the season, there's no way we'd be in this situation," he added.
"I thought they were incredible today, but it's not a day for incredible, it's too late, you're down, you're finished, it's over."
Granada's relegation ends a six-season spell in the top flight. They play Real Madrid at home in their next match on 6 May with fans having walked out of previous defeats in protest at how the club is being run.
Match ends, Real Sociedad 2, Granada CF 1.
Second Half ends, Real Sociedad 2, Granada CF 1.
Mikel Oyarzabal (Real Sociedad) wins a free kick in the attacking half.
Foul by Uche (Granada CF).
Jon Bautista (Real Sociedad) wins a free kick in the defensive half.
Foul by Sverrir Ingi Ingason (Granada CF).
Corner,  Granada CF. Conceded by Mikel Oyarzabal.
Hand ball by Juanmi (Real Sociedad).
Corner,  Real Sociedad. Conceded by Guillermo Ochoa.
Attempt saved. Sergio Canales (Real Sociedad) left footed shot from outside the box is saved in the top left corner.
Martin Hongla (Granada CF) is shown the yellow card.
Juanmi (Real Sociedad) wins a free kick in the attacking half.
Foul by Martin Hongla (Granada CF).
Foul by Zaldúa (Real Sociedad).
Andreas Pereira (Granada CF) wins a free kick in the defensive half.
Goal!  Real Sociedad 2, Granada CF 1. Juanmi (Real Sociedad) right footed shot from the centre of the box to the bottom left corner. Assisted by Sergio Canales with a through ball.
Attempt missed. Raúl Navas (Real Sociedad) header from the centre of the box is close, but misses the top left corner. Assisted by Sergio Canales following a set piece situation.
Ezequiel Ponce (Granada CF) is shown the yellow card for a bad foul.
Asier Illarramendi (Real Sociedad) wins a free kick in the attacking half.
Foul by Ezequiel Ponce (Granada CF).
Delay over. They are ready to continue.
Delay in match Uche (Granada CF) because of an injury.
Substitution, Real Sociedad. Jon Bautista replaces Carlos Vela.
Attempt missed. Yuri (Real Sociedad) left footed shot from outside the box is too high. Assisted by Mikel Oyarzabal.
Corner,  Real Sociedad. Conceded by Victorien Angban.
Attempt blocked. Sergio Canales (Real Sociedad) left footed shot from outside the box is blocked. Assisted by Zaldúa.
Attempt saved. Jeremie Boga (Granada CF) right footed shot from outside the box is saved in the centre of the goal. Assisted by Andreas Pereira.
Hand ball by Yuri (Real Sociedad).
Attempt missed. Mikel Oyarzabal (Real Sociedad) left footed shot from the centre of the box is close, but misses to the right. Assisted by Juanmi.
Offside, Granada CF. Jeremie Boga tries a through ball, but Gastón Silva is caught offside.
Foul by Zaldúa (Real Sociedad).
Jeremie Boga (Granada CF) wins a free kick in the defensive half.
Substitution, Real Sociedad. Sergio Canales replaces Xabi Prieto.
Substitution, Granada CF. Ezequiel Ponce replaces Adrián Ramos.
Attempt saved. Juanmi (Real Sociedad) right footed shot from the centre of the box is saved in the top centre of the goal. Assisted by Asier Illarramendi.
Goal!  Real Sociedad 1, Granada CF 1. Adrián Ramos (Granada CF) header from the centre of the box to the bottom right corner. Assisted by Dimitri Foulquier with a cross.
Attempt blocked. Adrián Ramos (Granada CF) right footed shot from outside the box is blocked. Assisted by Andreas Pereira.
Substitution, Granada CF. Jeremie Boga replaces Aly Mallé.
Offside, Real Sociedad. David Zurutuza tries a through ball, but Carlos Vela is caught offside.
Offside, Granada CF. Andreas Pereira tries a through ball, but Adrián Ramos is caught offside.
Tony Adams' Granada have been relegated to the Spanish second tier after a 2-1 defeat at Real Sociedad.