Fourth-placed Los Che travel to Sevilla on Saturday with a two-point lead over Real Sociedad and knowing victory would guarantee them Champions League football.
Anything less, though, and they would be relying on Sociedad to slip up at relegation-threatened Deportivo La Coruna.
Valencia moved into pole position with a 1-0 win over Granada last Sunday as Sociedad drew 3-3 with Real Madrid and Valverde said on the club website: "The truth is that I see my team are focused and, yes, before I detected a bit of euphoria.
"On Saturday we play a very important game against a team that are strong at home, while Real Sociedad play against a team that are fighting for their lives. We have to start from the premise that Real will win."
Sociedad are guaranteed at least fifth place and Europa League qualification, but below them the qualification picture is far from clear, with ninth place potentially good enough for a European spot.
Seventh place, currently occupied by Real Betis ahead of their trip to Levante, is definitely sufficient because Atletico Madrid - winners of the Copa del Rey - finished third and therefore will line up in the Champions League rather than the Europa.
But with sixth-placed Malaga and eighth-placed Rayo Vallecano currently banned from Europe next season pending appeals to the the Court of Arbitration for Sport, Sevilla in ninth are in a Europa League qualifying spot as it stands.
Getafe, who travel to Granada, and Levante are still in the hunt, too.
The fight against relegation has also gone down to the wire, with any three of the bottom four to go down.
Two points separate bottom side Real Mallorca, who host Real Valladolid, from fourth-bottom Deportivo.
Real Zaragoza are second-bottom, one point from safety ahead of their home match with Atletico, and striker Helder Postiga claimed his side will fight to the bitter end.
"When I walk through the tunnel at La Romareda I always read one sentence: 'Zaragoza never give up'. We will give the maximum to the end to honour the shirt," the Portuguese said
"Things can change, we must win and hope."
Celta Vigo are the other team in trouble, level on points with Zaragoza, and host Espanyol.
Jose Mourinho will take charge of Real Madrid for the final time at home to Osasuna as his turbulent reign at the Bernabeu comes to an end.
The Portuguese has not always been popular among his senior players, but midfielder Sami Khedira paid tribute to the departing boss with a post on his Facebook page which said: "I want to thank him for the opportunity he gave me at Real. I want to thank him for the support he has given me. He has always had my back, sometimes because I received criticism from the press! I want to thank him for all the time I was able to develop and mature as a player and a person at Real Madrid."
Champions Barcelona finish their season at home to Malaga, while Vallecano host Athletic Bilbao.
Sunday's La Liga Fixtures