Stoke midfielder Whelan escaped punishment for a two-footed challenge on City's Garcia in the 47th minute of the FA Cup fourth-round tie between the sides at the Britannia Stadium.
Webb took no action, not even awarding a free-kick for a tackle ITV analyst Andy Townsend described as a "red card every day".
Webb was close to the incident but the position of Garcia on the ground may have impeded his view of the moment of contact.
When asked about it, Barry said: "I'm not too sure. 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."
With the incident going unpunished at the time, there is a possibility the Football Association could take retrospective action.
The governing body will be able to determine that after receiving the referee's report.
The important factor will be whether Webb saw the incident or not.
Barry said: "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."