Ryan had started the first two La Liga matches for Valencia this season, conceding five goals, but was replaced by Brazilian Diego Alves for this match.
It is unclear who is Valencia's number 1 at this stage. Ryan returned from international duty with Australia this week, while Alves stayed in Valencia and completed all training sessions.
Ruben Castro's stoppage-time winner clinched the win for Betis, their first league success of the season and consigned 10-man Valencia to a third straight defeat.
The Betis striker fired home from close range in the second minute of time added on after Valencia had fought back from two goals down in the second half despite midfielder Enzo Perez's straight red card in the 50th minute.
Castro gave Betis a half-time lead with his 38th-minute opener and the visitors went two up through Joaquin early in the second period before goals from Rodrigo and Ezequiel Garay hauled Valencia level.
Betis, who had taken one point from their first two games, went ahead when Castro latched on to Cristiano Piccini's pass in the area to shoot low into the bottom corner.
The home side were reduced to 10 men early in the second half when Perez - already booked for a first-half foul on Darko Brasanac - was shown a straight red card for his challenge on Riza Durmisi.
It got worse for Valencia when Joaquin finished off a swift counter-attack with a neat finish into the bottom corner to put the visitors two up in the 54th minute.
But Valencia refused to buckle and carved out numerous chances before pulling one back through Rodrigo's angled drive in the 75th minute.
The home side were back on level terms three minutes later when defender Garay slammed the ball home from six yards after Betis had failed to clear a corner.
Nani and Munir El Haddadi both went close as Valencia pushed for the winner, but they were undone in cruel fashion in the second minute of stoppage time as Castro pounced from close range again after another Piccini assist.