However, the Uruguay international has explained that he agreed to move to the Galician side to get more experience.
"[My loan move to Deportivo] was a blow, because I would have loved to always be at [Real] Madrid," Valverde told Real Madrid TV.
"But then I thought about the opportunity to play with older and experienced players.
"I said yes. It cost me, but I really wanted to have my space and be alone."
Valverde went on to recall the day he learned that Los Blancos were interested in signing him.
"I dreamed of playing in a huge stadium where many people would shout my name," Valverde added.
"When Madrid asked about me it was a 'crazy' day.
"I was in the room and they called me to go to another room saying that Madrid wanted me.
"I wanted to be calm, but it was Madrid and I couldn't believe it when a person from Real Madrid came and told me they were interested in me.
"It's nice, it's spectacular, to get to the team I dreamed of and wanted to [join].
"I was leaving friends and family behind. It hurt a lot, but I couldn't pass up this opportunity."