(All of what I'm going to describe assumes you were at fault. If you were not found to be at-fault, then as ecmst12 said, don't worry about it. You would then just be considered to have been unlucky enough to get hit by the idiot who was at-fault.)
If you are at fault:
You are not quite understanding the situation here. The insurance company is not trying to "recoup their loss", your chances of getting into a wreck was already priced into the premium when they wrote the policy. Insurance works because of the law of large numbers. They made a bet on you not wrecking and "lost" that bet. They lost a lot of money on your policy, BUT they will "win" on a lot of other drivers who do not file a claim. Multiply that by tens of thousands of policies, and they can figure out how much they need to charge to be reasonably assured of making money from your premium and investment income after all claims are paid.
What's happening here is you are no longer the same risk you were a year ago. A year ago you were just someone with a clean record and supposedly had the same chance of having an at-fault accident as every other person with a clean record of your gender/age/marital status/traffic tickets/type and model of car/etc.
You are not that person anymore, if this was your fault then you are now a person who had an at-fault accident in the last few years, and you have the same chance (much higher than people with clean records) of getting into another at-fault accident as everyone else who recently had an at-fault accident with your gender/age/marital status/etc.
The insurance company has discovered that you may not have been as good of a risk as they once thought, and they will now want more money to cover themselves in future policies until you prove to them that you are a safer driver again by not having another at-fault accident for a few years. Similarly, when you turn that magic age of 30, many insurance companies will give you a big rate cut on the next policy, because you are not 29 anymore. For whatever reason, 30 year olds are safer than 29 year old drivers, and if they dont give the discount, the competition will.
When an insurance company begins to lose money overall on all risks, they just raise rates on everyone, inflation hits insurance too. In addition to that, they are constantly trying to figure out who is a safer or more dangerous risk, and give out rewards or surcharges accordingly.