That result has Lucas Alcaraz's side nervously looking over their shoulders again towards the relegation zone, with just four points separating them from the bottom three.
But no one at the club is panicking, and full-back Allan Nyom emphasised that everything would change with a victory over Villarreal.
"Our aim is to beat Villarreal to give us a points cushion," he told Marca.
"We have had very difficult games against Valencia and Athletic away from home, but if we beat Villarreal we will be in a good position again."
Alcaraz was also optimistic in his pre-match press conference, declaring that his side had every chance of beating fifth-placed Villarreal, even though the two teams are at opposite ends of the table.
"We have to respect the particularities of our opponents and focus on their strong points but we also have to remember ours," he said.
"They are difficult opponents, but in the same way that there is no guarantee you will beat a team below you in the league, there's no guarantee you'll lose to a team above you in the table."
Diego Mainz was sent off for Granada against Athletic and will play no part in the game, while forward Piti and defender Tiago Ilori are both doubts due to injuries.
However, Villarreal forward Ikechukwu Uche is now free to face Granada after the Spanish Football Federation rescinded the first yellow card he received in the 1-1 draw with Betis last Sunday, which led to him getting sent off in the game.
Villarreal fell six points behind Athletic in the race for fourth spot as a result of the draw with Betis, but defender Gabriel Paulista insists the team are not about to give up on catching the Basques so they can get back into the Champions League for the first time in three years.
"We have great players, a good coach and that makes us believe that we can still get into the Champions League," he told a press conference.
"It's difficult but we know we've got a chance.
"The first thing we need to do is get points at Granada, which will be a difficult game.
"The team is focused on this game and we go there with the aim of getting the three points - and we are confident we'll be able to do just that."