A stalemate ensued at the Greenhous Meadow just as it had when the teams met at Griffin Park in October.
The result ended Brentford's blistering run of five straight victories in League One.
Shrewsbury came closest to a breakthrough when a flowing move engineered by Marvin Morgan saw Connor Goldson set up Jon Taylor and, although the winger's shot beat goalkeeper Richard Lee, defender Harlee Dean headed off the line.
"It was a fair result and I'm very happy with a point," said Rosler.
"At this time of the year it's all about getting points, there's a lot of games and difficult conditions with the pitch although it was quite good to be honest for the amount of rain so I couldn't have asked for more.
"We had chances, they had chances, but in the end it's a very important point."
Brentford were more dangerous in the second half and Marcelo Trotta, the striker on loan from Fulham, came closest for the Bees when his powerful shot took a deflection but was superbly clawed out by Shrewsbury goalkeeper Chris Weale.
"We went to a 4-4-2 and went for it," added Rosler. "We had some good opportunities but they did as well on the counter. Taylor is a threat, Morgan is a threat, but we coped very well as a group.
"Compliments to Shrewsbury as they had a game plan at our place and we drew 0-0. Both teams were equal and we got a draw. I can live with that especially when you see the results from other teams."