The problem is that without seeing what you're doing, it's kind of hard to diagnose.

You may be moving too much. (unless you are top of web, that shouldn't be an issue)
You may be healing late and having your heals picked up by other healers first.(haste/reac)
Your gear may be sufficiently lower that throughput is an issue.
You may be using the same spells, at different(wrong) times/targets.
You may be simply not casting as many spells.
You may be doing some combination of the above.

But those are the things I would look at first.

There's been a lot of talk of this lately (and, quite frankly, since Cata brought in the new healing model), but shaman are tending to not have the same output as other healing specs. Whether it's because of skill or because people aren't playing them as much as other classes because they believe them to be suffering, or simply a case of the class being weaker is unclear.

That said, Jaba pointed out some very good places to start looking at your healing. Not knowing what your UI/healing setup is like, it's hard to say whether that could help, but it might do to look it over for yourself and see what you can cut out/add/change to improve performance.

However, you say that the other shaman is (are? didn't mention how many other shaman) using the same heals you are but simply getting higher numbers, and to me this sounds like a gear issue where your heals aren't hitting for as much. Or it could just be that the other healers in the raid are keeping everyone mostly topped off and you just happen to be using the same spells. It's hard to say, but I encourage you to keep at it :) Practice makes perfect, and that goes for healing, too. If you like it, you'll stick to it and the rest will come. Hope I helped.

It might be that your healing team has more healing power than necessary. While DPS can always go after bigger numbers, the healing for an encounter is necessarily capped by the amount of damage your raid takes. If your healing team's total output potential is higher, some healer(s)' output is not going to live up to potential. Sometimes, all the healers' output is lowered. Sometimes certain healers tend to get their healing in first and other healers see their healing drop disproportionately.

The first test of a healing team is whether bosses are dropping at the rate deemed reasonable for your raid team (based on time spent, dedication demanded, skill demanded, etc). If they are, the individual numbers of the healers is largely irrelevant (unless there's an extreme situation, like one healer doing 4k HPS).

If the healing doesn't seem sufficient in total, then it's time to dig a little deeper and try to really figure out where the discrepancy comes from. Obviously, it's a tough question, but the first step is to ensure you're being aggressive with your mana pool. Your mana pool plus your mana regeneration over the encounter is all "potential healing." If you wipe with mana left over, you left some potential on the table. If that's not an issue, then you need to start poring over spell choices and targets chosen to heal. That's where it becomes difficult. ;)

from my holy priest pov, problem lay most probably in your raid ....size

in 10 mans you are kinda expected to heal tanks time to time (if not as full time job) that apply for 25 of course as well but not nearly as often and lets admit it, disc/resto druid/paly are better suitable for tank healing when managing raid just fine
where resto shamans really shines is raid healing, ideal scenario when most of raid group can be found in one place begging for your rain and chains,, and thats the problem of 10 mans, you hardly find these situations, even if all melee, ranged and healers stand at one spot that just 8 ppl, not nearly enough to show your truly potential

from pure hps pov, our two shamans have no trouble toping meters in fight like beth, when especialy second phase is god blessing, lord ryo is another example, melee are usualy away but nothing chain cant handle and rain take care of poor ranged, what about angry bird, third phase oh we are all stack at one place, and dont forget Staghelm, you actually need all those ppl to stack up to force scorpion.p

if you not afraid of bit more bigger raid size, i would recomend giving 25 a go, this is place where resto shamies/holy priest are having their fun!.p

If you're reading replies to your post, send me a log of one of your raids if you've got one. Ideally one with a similar geared shammy also in the raid.

dj.clayden@gmail.com

I play holy pala, but maybe I can help you improve as shammy :)

You might also want to look at the balance of your stats and think about the type of damage that you have to heal. I'm certainly no Shaman expert (my main is a Druid), but I've healed with a Shaman and done a bit of reading up on them. I know that the Shaman mastery works best when players are at low health, but if you are healing targets that remain at relatively high health for most of the fight you will probably get more healing out of crit. (I think haste is generally considered better than either mastery or crit for Shaman, but you might want to check that.)

Anyway, my point is that if you have a lot of mastery and your raiders aren't dropping very low in health before being healed then you might want to drop mastery in favor of crit. Or, if people are dropping to low health, try stacking more mastery so you can bomb bigger heals on them. Also check to see what stats the other Shaman in your guild are stacking and if you're doing something differently you might want to try their gearing strategy.

The blog Life in Group 5 had an excellent post comparing Shaman mastery and crit: http://lifeingroup5.com/?p=2258

After you've done a bit of research you might want to go back to your raid leader and let them know that you've studied your class, changed things around, and want a chance to show how you've improved. Your initiative and desire to improve your gameplay should impress them, and hopefully you'll get the chance to prove yourself again.