Nicolas Jackson, Raheem Sterling and Noni Madueke were all wasteful or unthreatening in front of goal in a dominant first half for the Blues at Stamford Bridge on Saturday, with Mykhailo Mudryk and Armando Broja both out injured.
Ethan Pinnock and Bryan Mbeumo instead won the match as Brentford improved in the second half to make it just one win from the last 13 home Premier League matches for Chelsea.
Asked whether his side have enough goalscorers after spending over £400million on new players in the summer, Pochettino said: "It's obvious at the moment, no. So far, no.
"It's bad luck. [Christopher] Nkunku that proved he can score in big leagues like the Bundesliga was injured in the last pre-season game. This type of thing did not help.
"Then we need to recover Broja and different circumstances. Nicolas Jackson was affected for different reasons, but he's young and arriving this season and needs time to adapt.
"Of course that is obvious, and your analysis and some point, I think we agree."
A supporter was heard shouting "wake up and score a goal" at Jackson, which prompted a reaction from Pochettino.
He explained why he responded to the supporter, who was sat behind his bench. "It was a moment we all felt frustrated," he continued.
"After 40 minutes of playing really well and creating chances, we didn't score. This moment was a little bit down, the energy of the situation.
"He [Jackson] arrived to me and we talked about the position on the pitch and to find some solution and we gave direction to him.
"Because it was calm, one fan said, 'oh wake up' and started to abuse a little bit, I don't say that abuse but it's abusing.
"For Nico, he lost a little bit of focus. I said, 'come on, be focused here'. He repeat again and say, 'oh, let's stop talking this way, we need support, stay behind the team'.
"That's it, nothing more, very respectful and the fan was respectful, only he said wake up and the player took it in a bad way.
"It's normal because the player wanted to score, to provide a good thing - nothing more."
Cole Palmer was the one bright spot from a disappointing afternoon, which saw Brentford leapfrog Chelsea after their third successive win at Stamford Bridge.
The Blues dropped into the bottom half of the table but Pochettino was full of praise for his £40m signing from Manchester City, adding: "We are happy in the way he arrived.
"He arrived in the last moment of the transfer window, he's playing like he's here for 10 years and showing his character and personality."
Pochettino confirmed that Mudryk and Enzo Fernandez both pulled out of the match at the "last minute", but added that "neither are big problems".
Both had muscle issues and Fernandez's wife also gave birth to a new baby boy on Friday.