Warner appeared to take the gloveman's word after edging a catch off the bowling of Ben Stokes during the opening one-day international of the five-game series.
The batsman, on 22, started to walk off the field but waited at the boundary rope after the on-field umpires called for a review.
Sri Lankan TV umpire Kumar Dharmasena viewed the replays and instructed the on-field officials to recall Warner.
The replays on the video scoreboard showed doubt over whether the catch carried, although some senior England touring media went on Twitter to say Warner should have been given out.
Warner was eventually caught at long on for 65 off 72 balls after an opening stand of 163 with Aaron Finch.
"Looks like it has bounced up into the gloves from the fingers, but TV umpire says bounced off the ground. Very tough call all round I think," Mirror newspaper correspondent Dean Wilson said on Twitter.