The Gunners appeared to be coasting to all three points at Vicarage Road after Pierre Emerick-Aubameyang's first-half double.
Tom Cleverley took advantage of some slapstick defending by Sokratis Papastathopoulos to reduce the deficit, however, before Roberto Pereyra ensured a share of the spoils from the penalty spot after he had been brought down by David Luiz.
The Hornets – who had 31 shots on goal – can consider themselves unlucky not have claimed all three points, leaving Emery to hope the chastening experience will be of use to some of his side's younger players.
"We have some young players and they need to have experiences like today," he told a media conference.
"Matteo [Guendouzi] is young and very emotional; sometimes he needs to make some mistakes to improve. In the first half he made a mistake and they didn't score.
"When we are analysing the mistakes, we prefer to speak about them collectively. I have responsibility.
"I don't want to say it's the fault of one player or another. It's my responsibility to give them the confidence to execute our game plan."
The Arsenal boss was frustrated with his side's inability to deal with Watford's aggressive pressing and says improvements are needed quickly.
"The second half was going to be difficult as they changed their plan to push more than us," added Emery, who watched his side fight from 2-0 down to draw with Tottenham prior to the international break.
"If we could break that pressing, we could connect with our midfielders and have space to continue imposing our game plan. We couldn't control the match and break their pressing. They're a good team and in the second half they showed that.
"We also spoke about the need for calm to achieve what we wanted, and we did not do that. We need to work and improve things."
The draw leaves Arsenal seventh in the table, with eight points from five matches, while winless Watford remain bottom on two.