Stoke midfielder Whelan escaped punishment for a two-footed challenge on Javi Garcia during City's 1-0 FA Cup fourth-round victory over the Potters at the Britannia Stadium.
Webb failed to even award a free-kick but, when quizzed on the matter, Barry admitted that the referee had told him he did not have a clear view of the incident.
Barry said: "I think the referee said at the time - I spoke to him and he said he didn't have the right angle on it but Javi, in the changing room, said the player went in with both feet and caught his ankle so I think they showed that on TV too."
Given that the incident was unpunished at the time, there is a possibility the Football Association could take retrospective action.
Barry added: "I think there is a case. I think it's the rule now that if the referee doesn't see it but reports it, then they can have another look at it.
"But I don't want to speak badly against Glenn Whelan. He's a great pro and I'm sure he went for the ball."
Although Garcia played on after the incident, City skipper Vincent Kompany was less fortunate after suffering a calf strain during the first half of the game and will miss Tuesday's trip to QPR.
Barry said: "It was a little setback, mid-game, especially against a side like Stoke. Vinny's a big loss, but the lads who've come in have done a great job.
"I think his calf has been niggling him for a little while so this was one game too far. It's not ideal, so he'll have to have a scan and see how long he'll be out."