"We made fools of ourselves and we are ashamed, at least I am. I hope this does not happen again," the former Yugoslavia international told a news conference.
"We didn't deserve more. We didn't play as a team and our rivals have overcome us with a better attitude. There are no excuses."
Helder Postiga had given Valencia the lead against the run of play in the 10th minute, but despite Djukic having warned of the hosts' aerial threat before the game, they conceded two headers at set pieces either side of the break.
Espanyol's French forward Thievy Bifouma lashed a third at the end, giving a side expected to be fighting to avoid relegation in May, a first win this season.
After two rounds of matches Valencia, with aspirations to challenge for a top-four finish and the Champions League places, have only managed two shots on target according to Optastats, scoring from both.
They scraped a 1-0 win at home to Malaga last weekend.
"Perhaps we aren't as good as we think, and we should get down off the cloud," Djukic continued.
"Maybe we think we are stars, but what we have to do is get down to work. We didn't have the intensity needed to beat a rival like Espanyol. We swapped roles. They have been a side fighting for the Champions League, not us."
Djukic, a popular former Valencia player who helped the side to consecutive Champions League finals in 2000 and 2001, was recruited from Real Valladolid at the end of last season after Ernesto Valverde rejected the offer of a contract extension.