From the transcript:
Xavier: They captured her that day. Tortured her. Experimented on her. In her DNA they discovered the secrets to her powers of transformation. It gave them the key they needed to create weapons that could adapt to any mutant power and the result is the machines that have destroyed so many of our kind were created and it all started that day in 1973.
And later in the past:
Trask: This creature is extraordinary. Her genes could hold the key to mutation itself. I need more.
Agent: That's all they were able to scrape off the pavement in Paris.
Trask: More than blood. I need brain tissue, spinal fluid, bone marrow.
They didn't just copy her powers. They researched. They Experimented. They expanded what it could do. Same thing Apocalypse and Mr. Sinister and pretty much anyone in the Marvel Mutant universe has done to the X-Gene. Mystique, in the comics also had secondary mutations. It allowed to to gain a healing factor, mass-shift, morph into non-living things, and in X-Men Evolutions she could even transform into a Murder of Crows. She's basically biologically immortal. The comic Mystique is well over 100 years old, without any signs of aging.
Also consider, her DNA caused Hank to turn into the Beast. The power of the transformation wasn't just cosmetic or an illusion, Hank is physically changed.
They started with Mystiques cosmetic transformation, and using that, learned how to transform more of the genome, unlocking the rest of the X-Gene's power, which is to transform and adapt under (evolutionary) pressure. She's the starting point, not the final destination.
Additionally, remember that Trask has experimented on other mutants as well. When Mystique breaks into his office, she sees file after file detailing what has been done. The Sentinels are combinations of multiple mutant powers, with Mystique's power allowing the Sentinel to change when needed. The more mutants the Sentinels captured, the more that were experimented on, the more powers they could adapt.
Keep in mind, there are multiple types of Sentinels. In the DOFP time line, we see the first, Mark I sentinels, and the last, Mark X sentinels. There's a steady progression of technological changes between that time. They didn't immediately jump to the shape-shifting sentinels.