He is yet to oversee a La Liga win since taking charge in December, as Ruben Castro's second-half goal gave Betis a first win in 13 games.
Neville faced calls to resign following a 7-0 loss in the first leg of their Copa del Rey semi-final at Barcelona.
He refused to quit, but may now face more questions about his future.
The former Manchester United skipper's record in La Liga now shows four losses and five draws from nine games, as Betis secured only their second home league win of the season.
The first was against Real Sociedad, then managed by ex-Everton and Manchester United boss David Moyes, in September.
Veteran striker Castro, 34, struck the only goal of the game four minutes into the second half as he tapped in after on-loan Norwich striker Ricky van Wolfswinkel had driven the ball across goal.
Neville's side, who are now only four points above the relegation places, almost equalised immediately but an effort from ex-Manchester City forward Alvaro Negredo was cleared by defender Juan Manuel Vargas in front of an otherwise open goal.
Valencia were reduced to 10 men for the final few minutes when defender Jose Luis Gaya was sent off for pulling back on-loan Chelsea midfielder Charly Musonda which earned him a second yellow card.
Both sides had efforts ruled out for offside and Neville saw the last chance of a point disappear in stoppage time when Betis goalkeeper Antonio Adan raced off his line to deny Rodrigo as Valencia's scoreless run extended to three games.
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Gary Neville suffered another defeat as Valencia manager as a 1-0 loss at struggling Real Betis placed the ex-England defender under more pressure.