Bailly received treatment after colliding with Dean Henderson and was eventually replaced by Harry Maguire as the Reds secured passage to the FA Cup fourth round with a 1-0 victory to the Championship side.
The center-back has been in good shape recently, but his replacement has raised fears that another injury could stall his stop-start career at Old Trafford.
Still, Bailly told fans he was doing fine in a Twitter post: “Good job from the team to move forward in the FA Cup. I’m fine, it was just a hit. ”
United are preparing for a huge week playing Burnley on Tuesday knowing they will move up to number one in the Premier League table if they avoid defeat.
Ole Gunnar Solskjaer’s men will then travel to Anfield next weekend in a clash between the top two teams in the league.
Speaking on BT Sport after the win over Watford, Solskjaer downplayed fears Bailly could miss upcoming games thanks to concussion protocols, revealing it was actually a neck issue that forced the center-back to leave the field.
Solskjaer said: “It’s his neck, I think. His head is fine, but I haven’t spoken to him. There’s no concussion or anything like that. ”