The La Liga leaders failed to score in a Champions League group-stage match for the first time since 2012 as they were held in Greece on Tuesday.
Valverde praised his players for their efforts despite not getting the result they wanted.
"We were lacking a goal. We tried to get closer to their area on the basis of longer possession," he said.
"But they did a great job in defence and tried to hit us on the counter-attack, spurred on by their fans.
"You could see what amazing people there are here. We wanted to secure qualification but we failed.
"It was still a step forward, but not the one we wanted. The players emptied their tanks out there."
The clash marked a return to his former club for Valverde, who coached Olympiacos in two stints in 2008-09 and 2010-12.
Despite being on the opposite side of the fanatical Olympiacos support, Valverde praised the fans.
"The answer to everything is how well our opponents played. They stuck tight together as a unit. We were up against an opponent that did their job well from start to finish," he said.
"I always had this atmosphere in my favour and today it was against me. I know what the Champions League means to these fans because I've experienced it myself many times.
"It may have come as a surprise to people coming from Barcelona, even though everyone knows how intense Greek football support can be. It was extraordinary. Really nice."