Yes, generally speaking, springers need to be held a little differently that any other type of gun. Due to the spring and piston lunging forward when you fire it, a springer has a weird bit of reverse recoil. It is so bad on magnum springers (1000fps and over) that it can kill scopes that aren't designed to handle it.
Most of the time, a loose hold is needed. Support the forend with your off hand, but don't grip it tightly. Also a loose grip with the shooting hand. You want to let the gun recoil back and forth while still keeping it on target. This is called the "artillery" hold (think of how a howitzer or whatever recoils and moves forward back into battery).
Also you need to watch your follow through. Since even a magnum airgun does not shoot as fast as a rimfire or centerfire rifle the pellet is in the barrel for a longer time so keeping the gun on target even after letting off the trigger is a good thing to remember. It takes practice and patience.
I have a few low-powered springers (600fps) and even those require a different hold than I use on my Crosman pumpers or .22 rimfire rifles.
If you just got it, did you clean the barrel out before shooting? There is stuff in the barrel for shipping and storage that will affect accuracy.
Then again, check the crown. Maybe there is an issue there.
Gamos are known for their bad triggers. There are things that can be done to improve them though.
I had a Gamo Shadow 1000. I could shoot it fairly well for plinking, but there just wasn't any chemistry with it. I gave it to my dad (he's 66) to try. Rested, he's getting quarter-sized groups at 25 yards with it using Gamo Rocket pellets, and that's without a trigger tune.