Unai Emery’s side seemed to be cruising to their second away win of the season at Vicarage Road thanks to a first-half double from Pierre-Emerick Aubameyang.
But they surrendered a two-goal advantage after the interval as Quique Sanchez Flores’ side fought back for a 2-2 draw, with Roberto Pereyra earning the hosts a point with a late penalty after he had been tripped by David Luiz.
It was a calamitous ending to the game for Arsenal, who would have moved up to third in the Premier League with three points, and things could have been worse had Abdoulaye Doucoure not fired straight at Bernd Leno in injury time.
Defensively, the visitors were a mess throughout, with Watford having 31 shots on goal during the 90 minutes.
But Sokratis has insisted he was the man who cost Arsenal victory, due to the mistake he made to gift Tom Cleverley the goal which made it 2-1 soon after the interval.
“I think that I cost the game for the team,” said the Greece international centre-back. “It was my mistake for something simple that I don’t have to do.
“I think this was why we lose the three points.
“I don’t want to speak about others. It was my mistake and this cost the game. Nothing else.
“The other guys tried their best. I didn’t have to do this mistake. Without my mistake, we would take the three points.”
When asked if he had apologised for his error, which came when Arsenal were trying to play out from a goal-kick, Sokratis added: “Of course. I apologised because I cost the game for the team and I have to work harder.
“I know up to this moment I didn’t have a mistake, I didn’t do nothing. Everything was near too perfect.
“But defence is no risk and it was my mistake.”
From the moment Cleverley took advantage of Sokratis’ error, Arsenal had little answer to the constant wave of attacks that Watford unleashed as the second half wore on.
An equaliser seemed inevitable and it finally arrived when Luiz tripped Pereyra with 10 minutes remaining, the third penalty Arsenal had conceded in their last three games.
“We didn’t have the same pace in the second half as in the first half,” Sokratis admitted.
“But if we didn’t do these mistakes, I don’t think we draw.
“Of course they had other chances to score more, but if we didn’t make these mistakes then nothing happens.”