Rodrigo scored the only goal midway through the first half as he blasted into the roof of the net from Ferran Torres’ clever pass.
Ajax desperately pushed for the equaliser they needed with Lisandro Martinez and Hakim Ziyech forcing late saves from Valencia keeper Jaume Domenech.
Valencia had defender Gabriel sent off in injury time for clashing heads with Dusan Tadic in a very tense finale in Amsterdam.
Ajax were seconds away from reaching last year’s final before Lucas Moura’s injury-time strike sent Tottenham to the final instead.
Frenkie de Jong and Matthijs de Ligt were among the stars of that team to leave last summer and they have not been the same since.
Two defeats at home – by Chelsea and Valencia – and a 4-4 draw at Stamford Bridge have ultimately cost them.
Valencia go through as group winners, with Chelsea in second after their 2-1 win over Lille. Ajax drop into the Europa League last 32.