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United was dealt a massive blow earlier this week with the news Christian Eriksen will potentially be out for three months due to an ankle injury caused by a heavy challenge from Reading's Andy Carroll.
The Denmark midfielder had been one of United's key players due to his creativity, as reflected by his haul of nine assists being bettered by no one else in the squad.
United moved quickly to bring in Sabitzer on loan from Bayern Munich until the end of the season as a replacement, with the Austria international's arrival appearing even more necessary after it emerged Scott McTominay is also facing a short spell out.
Ten Hag was thrilled to get the deal done, and he has high expectations for the former RB Leipzig star, despite him struggling to make much of an impact at Bayern.
"We're really happy with that transfer because we need it after Donny [van de Beek] dropped out, now [Christian] Eriksen for a longer time, for a short time Scott McTominay is not available," Ten Hag said after Thursday's (AEDT) 2-0 Carabao Cup semi-final second-leg win over Nottingham Forest.
"To bring a quality player in on deadline day, that is difficult. We got this opportunity.
"I know the player for a long time from Salzburg, especially Leipzig, [where] he performed fantastic. I expect the same here.
"He has a great attitude, he's the right age. I'm sure this opportunity will motivate him and he will perform for us."
Among the big talking points from the win over Forest was the comeback of Sancho, who had not played for United since 23 October.
The England international had been absent due to "circumstances with fitness and mood", which even resulted in him spending a period away from the club.
He played the last 27 minutes on Thursday, receiving a huge ovation from the Old Trafford crowd, and Ten Hag was thrilled to have such a talented player available again.
"It was great for Jadon and the fans cheered him and gave him a loud applause, and that's great and he sees how the fans like [him], give him this love," the manager continued. "So we are happy with that. We need to keep that connection with the fans and we need that all season.
"He has really high standards, he has great capabilities to contribute to our team and I think, especially now the team is improving, we are playing more in the opponents' half and I think his capabilities are coming more in front.
"He can act on them more because he will have more touches on the ball and that gives him the best platform to perform.
"Most important players enjoy football, which gives energy, that gives them the motivation to act and to perform. I think it was great, the reception from the fans to him, and also that will give him even more a push to continue in the way he's now acting.
"He's just started again, a restart. He's [been] back at Carrington [United's training base] for two weeks, we see that smile and hopefully he can keep that and contribute to the team because when he is in good form, he is really important for us.
"I hope, same as [Anthony] Martial, when you are all the time available and play often together with the players we have now in the midfield and front line, our attacking plan will improve and create more chances, then it's a process players enjoy more and are better motivated to work together."
United is next in action on Monday (AEDT) when it hosts Crystal Palace in the Premier League.