Nearly 10,000 fans paying as little as B£1 under a 'pay what you can' promotion saw Marcello Trotta's first-half volley clinch the points against an adventurous Shrewsbury side.
"We were in our shell in the first half, but after the break we started to play and had a couple of chances late on to get back in the game," Turner said.
"For around 50 minutes I thought we did very well, but you have to have bodies in the box and movement and we didn't.
"We gave it a right go in the second half but our problem is scoring goals."
Defeat saw the Shrews slip to 18th in the table but Turner said: "If you look at the times we've lost, it's very rare that we do so by more than one goal.
"We have come to a good side with very good players in front of a big crowd and given it a really good go, but their goal summed up what we need to be doing.
"Their player got across our man and sidefooted it home. That was the difference."
Turner added: "It is disappointing when you look at the table, but we will keep working hard and trying to do the right thing."
Unfortunately for the Shrews their ambition was undone when Marcelo Trotta was in the right place to smash home at the near post after a jinking run and cross from Kadeem Harris in the15th minute.
The Italian almost made it two just before the break when he was played in by Adam Forshaw, but his rising drive was tipped wide by Shrews goalkeeper Chris Weale.
John Taylor gave the visitors their first attempt on goal just before the break, but his low drive was easily saved by David Button.
The goal Brentford wanted to seal the points almost came in the dying minutes, but substitute Sam Saunders rolled a low cross wide after good build-up play from Clayton Donaldson.