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."
It is the second time this month controversy has surrounded a tackle in a City match after captain Vincent Kompany was sent off at Arsenal a fortnight ago. City successfully appealed against that red card and had a ban overturned.
But City are again facing the prospect of a spell without Kompany after the Belgian suffered a calf strain in the first half at the Britannia.
The club are still to learn the full extent of the problem but the defender has already been ruled out of 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."