Domingos Paciencia was at a loss to explain his side's defeat, whilst Ernesto Valverde admitted it was a ‘complicated’ victory.
The Turcos were 2-1 up at half-time against Los Che but saw two of their players sent off, before going down to a pair of late goals from Nelson Valdez and Ricardo Costa.
But the 44-year-old could not fault his team's effort during the 90 minutes.
“It is not easy to explain what happened here,” he told a Press conference. “We've been on a bad run, and we have to work hard to change the situation we find ourselves in.
“We did battle, but when you make errors like we did against a top opponent, you're going to get punished.
“The game was a different one after the first sending off – playing with 10 men against a team like Valencia is tough.
“But we've lost the game because of us, because of the mistakes we've made.”
Valverde meanwhile conceded that the home team made is difficult for his men, despite having two players sent off.
“That was a very important victory for us,” he told a Press conference. “We knew it was going to be a complicated match and Depor proved that with the spirit they showed.
“In the first half they created a lot of chances, but in the second I think we dominated them. We played against nine men [after Silvio and Paulo Assuncao were sent off] but we should have seen the game off before then.
“We still have to improve a lot of things, but everything's better with a win.”
See the latest La Liga predictions and betting tips with Eurotips.co.uk