There are three reasons you go out of mana.
1. People are taking too much damage. Tank may be undergeared. Not using enough crowd control. People standing in fire.
2. It is taking too long. Naturally the longer it takes to kill things, the more damage done to you while it happens. Lasting a one minute pull is significantly easier than lasting a 5 minute pull.
3. You are doing things incorrectly. Using the wrong spells. Spec or gearing incorrectly. Not prioritizing correctly (i.e. dispelling things that don't need to be dispelled is one good example).
Could you provide a link to your armory as well so we can see if there are any issues with spec, or other decisions you have made that may impact your efficiency.
Without seeing your character specifically all I can offer is very generic advice that "may" help. This is the most mana efficient restoration spec. 3/3 Furor and 2/3 Moonglow is the highest level of efficiency you can run.
Naturally there are tradeoffs to taking this spec, when you're mana issues aren't as bad you can drop talent points in the Balance Tree (Moonglow is ALWAYS weaker than Furor, never drop Furor as Restoration) and reallocate them to other talents diserable in the Restoration Tree.
"In anything, if you want to go from just a beginner to a pro, you need a montage." /w TankSpot WTB Montage for Raiders.