Rose, 50, is still winless as Bournemouth boss, with one loss and three draws from their opening four Premier League games.
Kevin Schade gave Brentford the lead in the 34th minute only for Justin Kluivert to level things up four minutes later.
The next two goals were a similar story. This time, Marcus Tabernier gave the home side the lead, then, four minutes later, Schade got his and Brentford’s second.
Bournemouth now sit down in 15th, but despite his side’s frustrating start, Rose is remaining upbeat.
Speaking to BBC Match of the Day, Rose said: "We were behind for the first time this season, we reacted well, and lucky me, we didn't concede a late goal.
“We had more chances, more possession, we were the best team.
"Brentford is a tough opponent, they are good for second balls and have quite big guys and ballers as well. I liked how we competed, the way we defended in most situations.
“I like the way we attacked, our attitude. We were unlucky in a couple of situations, so we just get a point."
Rose and Bournemouth will be hoping to get their first Premier League win as they welcome former boss Andoni Iraola on Sunday, September 20th.