Cpl David Allison, of The Royal Welsh, said the men had wanted tea or coffee to "calm our nerves" during rehearsals for Cpl Michael Thacker's funeral.
More than 40,000 people have backed a Facebook campaign calling for Browns Independent Bar to be boycotted.
The bar, which has a policy of not serving people in uniform, apologised.
Owner Ken Brown said the soldiers would have been served if staff had known the funeral was taking place.
Cpl Thacker, 27, of 1st Battalion The Royal Welsh, died on 1 June after being shot while manning an observation post in Helmand, Afghanistan.
The funeral for the soldier, who lived in Keresley, Coventry, with his wife Catherine and two-year-old daughter, took place at the city's cathedral on Monday.
His brother Matthew, a member of the same battalion, was among the pallbearers refused service at Browns Independent Bar.
Cpl Allison said they went into the Earl Street bar during a 40-minute break and did not want alcohol.
'Little bit worse'
He tried to be served after two other soldiers were refused.
"The lads that went in, they [staff] basically said that they couldn't come in as you're in fatigues and we won't serve you," he said.
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