Los Che currently sit two points behind fourth-placed Real Sociedad with four games to play and with Champions League football their objective, Valverde is wary of the tightrope his team are walking.
"We want to qualify for the Champions League and we cannot fail. We have no margin for error," he told Marca.
"We face Rayo Vallecano, who play attacking, clinical and positive football, next and they won't be easy.
"Since taking over I have always thought we had a chance to climb up the table and qualify for Europe. We have been united for some time and we have opened up an important gap between the rest of the sides fighting for a European place."
Valverde went on to lament the loss of Sergio Canales to a long term injury earlier this term, while he downplayed doubts regarding captain David Albelda's place in his side.
"Canales was out for a long time with an injured knee. It is normal that he found it hard to get back into the rhythm of playing. This is why he's had difficulties and for the team it is unfortunate," he continued.
"Players always have to be ready to play when called upon. Albelda has played in some games, others not. But, there are no doubts, we are sure of his abilities and what he can give us."