The 28-year-old started his fourth successive game at left-back against Villa after returning from a five-week absence in the 4-2 win at Newport County on January 28.
But Ten Hag was forced to replace Shaw with centre-back Victor Lindelof at the break, which contributed to an uncomfortable second half against Unai Emery’s dangerous side.
Scott McTominay netted an 86th-minute winner off the bench to add to Rasmus Hojlund’s early opener after Douglas Luiz fired the hosts level after the restart.
Shaw’s early substitution left a sour note on a momentous triumph, though, which was Ten Hag’s first away win from home against a top-nine outfit.
After full-time, the Dutchman confirmed that he took Shaw off as a precaution due to “some complaints” that weren’t worth risking.
“[Shaw came off as a] precaution. He had some complaints, and we can’t take any risks with him because he’s had many injuries in the past,” Ten Hag told Sky Sports.
“We’ll have to see how it goes in the next few days. It’s not an advantage to lose him. Everyone knows my philosophy to have left-footers at left centre-back and left-back.
“Lisandro Martinez and Luke Shaw are both left-footed, and we also haven’t had Tyrell Malacia for the whole season.
“So for the whole time, we have had to make compromises, and it is not to our advantage. But today, we managed it, and hopefully, it’s not too bad with Luke.”
Ten Hag openly admitted that his system couldn’t fully thrive without left-footed players to balance United in the build-up. But Shaw, Martinez, and Malacia’s absences leave him with no such options.
The welcome returns of Shaw, Martinez and Casemiro in January have sparked United’s best run of form in an injury-stricken season.
Ten Hag’s side have won four consecutive games for the first time this campaign, triumphing in seven of their last nine in all competitions.
With a trip to Luton Town and a home clash against Fulham next up before the FA Cup fifth-round tie at Nottingham Forest this month, the gap could become even more narrow before March.