Allen ruptured an Achilles tendon during the first half of the 5-1 Championship thrashing of Hull City at the bet365 Stadium.
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The 29 year-old will sit out the rest of the domestic season and will be unavailable to Ryan Giggs as Wales attempt to emulate their achievements of four years ago, when they reached the semi-finals in France.
"It's devastating for us and devastating for the boy. Not only will he miss the rest of the season but obviously miss Euro 2020 as well," O'Neill said via Stoke's website.
"He's a great lad and when you're a coach and a manager you want the good lads to get the rewards and do well in the game. Joe's a low-maintenance player but a high-output player.
"I know what it means for him to play for Wales and obviously we [Northern Ireland] played them in 2016 as well and he had a fantastic tournament then. I'm sure he would have been looking forward to the finals and a chance for him to show again that he's a top, top international player, which he's proven to be in the past. It's taken a bit of the shine away for me.
"I kind of feel like I did when Chris Brunt got injured before Euro 2016 and missed it. These things don't come around often in players' careers so when it's taken away from them cruelly with injury it's not very nice."