Udogie produced a magnificent assist for the second goal in Tottenham’s 2-0 win at the Vitality Stadium on Saturday, but looked in pain with a foot injury in the 82nd minute.
He was replaced by Ben Davies for the final eight minutes of the match, but Postecoglou has said it was nothing serious.
“I think he just kicked the ground, from what I understand”, Postecoglou said.
“He didn’t want to come off, but at that stage the way the rules are at the moment, they go off for 30 seconds and I thought it was better putting Benny on and keeping the tempo up in the game for us.”
Postecoglou added: “Just speaking to him now, he’s fine.”
Udogie has started all three of Spurs’s matches at the start of the new Premier League season.