Villa looked to be consolidating fourth position after goals either side of half-time from Ollie Watkins and Morgan Rogers put them in the ascendency.
But they hit the self-destruct button as three goals in nine minutes from Mathias Jorgensen, Bryan Mbeumo and Yoane Wissa saw Brentford turn the game on its head.
The hosts had to rally and a Watkins header rescued a point, but the result handed the impetus to Tottenham in the race for guaranteed Champions League qualification.
Watkins was scathing in his assessment after the game, saying Villa lack the "maturity or game intelligence", and Emery responded.
"We are disappointed and frustrated because we played very well until the minute 60 and after the minute 75, but in 10 minutes in the Premier League we know we can lose everything we have built before," Emery said.
"The mentality of the team we always have to work and increasing and be demanding, this is a process.
"Today, everybody is a little bit upset and not understanding clearly what happened.
"I will work with the players and tell them how we can continue in our way, being successful like we are, with 60 points after 32 games is more than our expectation before.
"But we have to be demanding to compete but we can draw a match like today when we lose a little bit of focus in the moment.
"The first 60 minutes I played like I really want, like we have played here before when we won a lot of matches in a row, it was completely difficult to understand how we played afterwards. It is my responsibility and I will work on it."
Brentford boss Thomas Frank has no issues with Ivan Toney and Nathan Collins' heated exchange at the end of the match.
The team-mates were angrily disagreeing with each other after the full-time whistle, with Toney seemingly unhappy about Collins not passing to him.
Asked what it was about, Frank said: "I don't know, I was over there speaking to them but I don't know exactly what it was and I don't really care.
"I know it is two very competitive people that want to win a match. I don't know exactly what it was the situation, but we have a very good culture and a united team and it is OK to have a little bit of friction.
"They will sort it out no problem."
Their disagreement could have been born out of Brentford's winless run extending to nine games as they failed to see it out after taking the lead.
"Fantastic game and brand for the Premier League, this is showing why it is the best league in the world and the most entertaining," the Dane added.
"Probably Unai and I would say we both should have won the game, both can argue well for why we should, OK in the end it's a fair result.
"I think it is a fine point but it is two points dropped when we are leading in that situation and we haven't been able to get over the line. But the performance is another step in the right direction."
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