The 25-year-old required stitches after a head clash in the 21st minute and returned to the pitch sporting a heavily bandaged head.
Despite the heavy knock, Hojbjerg would play on until the 62nd minute as he showed his willingness to play through the pain for his new club after a summer move from Southampton.
Mourinho admired the spirit of his Denmark international and had mixed feelings about a double pirouette he performed in the first 45 minutes.
"We were having a laugh at half-time and we were all calling him Zidane. Very nice but don't do it again Pierre!" Mourinho said in his post-match press conference.
"He's a very good player, a good leader and a captain without the armband."
Another player that caught the eye for Spurs against LASK was debutant Carlos Vinicius, who claimed two assists and created an equal-game high five chances.
The 25-year-old scored 18 league goals for Benfica last season and Mourinho was happy to see his new player begin his adaption to a new set-up so strongly.
"He played well but he can do better. Not easy to not speak English so the adaptation to the group isn't an easy situation," Mourinho said about the young Brazilian.
"Different football, different way to play, how we want to press. It's about learning. But with these circumstances, first match he did well.
"Only thing that was missing was one goal. Showed he's more than that and that he can play with Harry Kane as well."
Gareth Bale also made his first start for Tottenham since sealing a loan move from Real Madrid and conceded after the match he's still getting back up to speed after struggling for game time in Spain.
Spurs next face Burnley in the Premier League on Monday and have now gone 10 matches without defeat. Tottenham's strong start to the season has also seen them score 31 goals in all competitions so far - five more than any other Premier League side.