Unai Emery's men looked to have secured a 1-0 away win until Ruben Castro grabbed two dramatic goals in injury-time to give the home team an important victory.
However, Pablo Hernandez has stressed the importance of making sure that there is not a repeat showing in the future.
"This happens in football but we have to learn our lesson and make sure it does not happen again," the 26-year-old told Marca.
"We prepare for every game, look at the opposition's strengths and weaknesses yet small details can escape us at important times. Yesterday we had to kill the game in the final minutes.
"We controlled the game for 90 minutes and did the hardest part by getting ahead but we let it escape and felt bad after being so close to victory."
Valencia are next in action on Tuesday when they face an away trip to Cadiz in the Copa del Rey, a club the player spent a season on loan at during the 2007-08 season.
"I spent an important season of my career there, they helped me make the transition I needed to. It's a club and a city I will always be grateful to," he added.
Pablo Hernandez has made 18 appearances for the club this season in all competitions, scoring twice in the process.
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