The chancellor said she was "not satisfied with these numbers."
"For too long, our economy has felt stuck, with people feeling like they are putting in more and getting less out," Reeves said.
She added that she was determined to ensure the government supports people "struggling with higher bills and the cost of living challenges, deliver economic growth and build an economy that works for, and rewards, working people."
In a post on X, the shadow chancellor said that inflation running at nearly double the Bank of England's target was "pushing up the cost of living and punishing those Labour promised to protect".
Stride claimed national insurance increases, government borrowing and not having "the backbone to reduce spending" were all contributing to inflation.
The overall inflation figure for September matters more than most other months.
That's because the government usually uses this as the benchmark for the benefits uprating in April.
It means millions of people depending on benefits are likely to see a 3.8% increase in their payments next year.
The state pension will rise by more, because the annual increase for that is determined by the so-called triple lock.
This guarantees that the state pension goes up each year in line with either inflation, wage increases or 2.5% - whichever is the highest. September's inflation figure of 3.8% is below average earnings for the relevant period (4.8%) which means the rise in wages will decide the state pension increase.
The inflation figures for the past three months were the joint-highest recorded since January 2024, when the rate was 4%, according to the ONS.
Inflation in the UK remains well below the 11.1% figure reached in October 2022, which was the highest rate for 40 years.