By scaling up the digestive wind of cows, they estimate that the population of dinosaurs - as a whole - produced 520 million tonnes of gas annually.
They suggest the gas could have been a key factor in the warm climate 150 million years ago.
Fossil evidence suggests the herbivores lived in herds
Recognisable features include long necks, long tails and relatively small heads
David Wilkinson from Liverpool John Moore's University, and colleagues from the University of London and the University of Glasgow published their results in the journal Current Biology.
Sauropods, such as Apatosaurus louise (formerly known as Brontosaurus), were super-sized land animals that grazed on vegetation during the Mesozoic Era.
For Dr Wilkinson, it was not the giants that were of interest but the microscopic organisms living inside them.
"The ecology of microbes and their role in the working of our planet are one of my key interests in science," he told BBC Nature.
"Although it's the dinosaur element that captures the popular imagination with this work, actually it is the microbes living in the dinosaurs guts that are making the methane."
Methane is known as a "greenhouse gas" that absorbs infrared radiation from the sun, trapping it in the Earth's atmosphere and leading to increased temperatures.
Previous studies have suggested that the Earth was up to 10C (18F) warmer in the Mesozoic Era.
With the knowledge that livestock emissions currently contribute a significant part to global methane levels, the researchers used existing data to estimate how sauropods could have affected the climate.
Their calculations considered the dinosaurs' estimated total population and used a scale that links biomass to methane output for cattle.
"Cows today produce something like 50-100 [million tonnes] per year. Our best estimate for Sauropods is around 520 [million tonnes]," said Dr Wilkinson.
Modern methane producers
Microbes in the stomachs of "ruminant" species produce methane gas as they break down vegetable matter which is released as flatulence
Methane trapped in the Earth can also be released during drilling for natural gas
Current methane emissions amount to around 500 million tonnes a year from a combination of natural sources, such as wild animals, and human activities including dairy and meat production.
Expressing his surprise at the comparative figures, Dr Wilkinson added that dinosaurs were not the sole producers of methane at the time.
"There were other sources of methane in the Mesozoic so total methane level would probably have been much higher than now," he said.