Marcelino's Valencia dominated the game but struggled to find a breakthrough, with Valladolid goalkeeper Jordi Masip saving Rodrigo Moreno's second-half penalty.
Santi Mina missed from close range before Valencia captain Dani Parejo eventually put his side ahead in the 71st minute.
However Alcaraz's brilliantly-hit equaliser in the 82nd minute kept Valencia provisionally ninth, upsetting frustrated fans in the Mestalla who whistled at their team at the end, while Valladolid are 15th.
"I think the team had a great game but we were not very accurate in front of goal," said Rodrigo.
"I apologise to my team mates for missing the penalty. We have to keep working. The team did great work overall. We had three great chances, we are all a bit responsible (for not finishing them)."
(Reporting by Rik Sharma; editing by Clare Fallon)
