Everton full-back Coleman was given oxygen and carried from the field on a stretcher after being caught in the 69th-minute of Friday's fiery World Cup qualifier between the Republic and Wales in Dublin.
The Football Association of Ireland confirmed after the goalless draw that Coleman had broken his right leg and the 28-year-old is expected to undergo surgery on Saturday.
Wales manager Chris Coleman said Taylor had gone into the Republic dressing room after the game to see the Ireland captain, although he did not think he had managed to do so.
Taylor spent eight months out of the game after breaking his ankle in 2012 and midfielder Allen said the Aston Villa defender was devastated by the incident.
"He's in bits to be honest," Allen said. "Tayls is one of my best mates and he's a great guy. He's really disappointed that one of his tackles has ended up getting someone hurt.
"But unfortunately in football these things can happen. There was no malice in the tackle and he certainly wouldn't have intended to hurt anyone.
"I know him as well as anyone and I think everyone is disappointed, and from Seamus' point of view it doesn't look great."
Allen was involved in the game's first flashpoint just before half-time when he was caught by the swinging forearm of Stoke team-mate Glenn Whelan.
The two sets of players squared up to each other and, as the action became more fraught, the Republic felt Gareth Bale was fortunate to escape with a booking for his goalmouth challenge on John O'Shea.
Moments later Taylor went in hard on Coleman and Italian referee Nicola Rizzoli did not hesitate in brandishing a red card.
"He (Whelan) has given me assurances that he didn't mean it," Allen said of his club colleague. "It happens when you come up against players you know, team-mates, and there's no hard feelings at all.
"I'll have to see it back. At the time I thought I was caught by an elbow. Who knows?"