The RAC Foundation said the increase in casualties across Britain is a reminder that more work needs to be done to improve road safety.
Figures from the Department of Transport show 2,901 casualties were reported on Hampshire roads in 2022 – up from 2,695 the year before.
But it was down from the 3,060 road casualties reported in 2019, before the pandemic.
The data also shows more people were killed on the area's roads, with 37 deaths last year.
In 2021, 35 road deaths were reported.
Across Great Britain, 1,711 people were killed on roads. It marked a 10% jump from the 2021 but was down slightly from 1,752 in 2019.
Edmund King, director of the AA Charitable Trust, said: "Every death on our roads is a tragedy and it is worrying that after the pandemic, road deaths are rising.
"It is a preventable tragedy that a fifth of people who die in cars on our roads are not wearing a seatbelt.
"There needs to be concerted and targeted education to reach those drivers who choose to risk their lives for the sake of a two second action.
"It’s on all of us to eliminate deaths and casualties on our roads. As well as having more cops in cars to catch people in the act, road users need to take responsibility when heading out on the roads."
Overall, there were 135,480 casualties last year – up 6% on 2021, but down 12% on pre-pandemic levels.
Last year's figures include 28,031 people who suffered serious injuries on Britain’s roads. In Hampshire, 812 people were seriously injured.
RAC road safety spokesman Rod Dennis said: "Confirmation that last year saw a rise in the number of casualties on our roads is a chilling reminder that there remains so much work to do be done to improve road safety in the UK, even if statistically we have some of the safest roads in Europe.
"It’s time the Government turned the dial up on tackling these issues which, while complex, result in hundreds of people losing their lives every year."
A DfT spokesman said: "We welcome the continued decrease in road casualties compared with pre-Covid levels, with our roads being some of the safest in the world.
"Nevertheless, we continue to work tirelessly to improve road safety through our world-renowned Think! Road safety campaigns and £47.5 million safer roads fund, so local authorities can also work to keep road users safe."
Outside of coronavirus lockdowns there has been no significant improvement in road crash fatality figures since around 2010.