The 32-year-old suffered an injury-plauged first season at Old Trafford, managing just 18 Premier League appearances, before being banished from the first team altogether by Mourinho back in the summer.
Schweinsteiger, in spite of making a return to the first team, completed a move to MLS side Chicago Fire on Tuesday after managing just one start all season.
And Low, speaking ahead of his side’s clash with England in Dortmund on Wednesday, noted that Mourinho would have benefitted from using German this season.
“We spoke some weeks ago and he said in training he has given everything he has got,” he said.
“For a while there was some light on the horizon, but it was just not to be at Manchester United.
“I saw a few of United’s games. As a midfield organiser, I think United could have done with Schweinsteiger in a few games.”
The very fact that Schweinsteiger opted for a move to the MLS is in itself an illustration of his fading capacity to compete at the top level. Numerous European sides would have been chomping at the bit to secure the midfielder’s services, but he chose the US – a place of semi-retirment for depleted legends of the game – instead.
He would have known better than anyone that his days at top were numbered following a frustrating debut campaign in England, and he deserves nothing but respect finding a club that suits him, as opposed to trying to end his career as a token squad player at a bigger club.