The Denmark international has been ruled out for at least three months with an ankle injury suffered after a reckless tackle from Carroll during United's 3-1 win over Reading in the FA Cup fourth round on Saturday.
Carroll wasn't booked for the tackle on Eriksen, but was later sent off after receiving yellow cards for two other late challenges and Ten Hag was less than impressed with the performance of the former Newcastle United and Liverpool forward.
"I think football has to set limits, restrictions, that protect the players," Ten Hag told a news conference on Tuesday. "What football wants is the best players to be available on the pitch.
"This is a tackle, and the two tackles after it, that don't belong on a pitch, because there is a high risk of injuring your colleague. So it's worse and I'm left wondering about that."
United's medical staff are still assessing Eriksen, but expect the midfielder to be out until at least late April.
Ten Hag will have to juggle his squad in four competitions during the second half of the season, starting with the Carabao Cup semifinal second leg against Nottingham Forest at Old Trafford on Wednesday.
United are in pole position to reach the final at Wembley after winning the first leg 3-0 at the City Ground and Ten Hag is expected to make changes for the return fixture.
"We have a perfect chance to go to Wembley and to bring a trophy in and therefore we have to focus," said the Dutchman. "We have to gather the energy, have a good game plan and we have to do it with the players available.
"We are in momentum and want to keep the process going. Nottingham Forest are a good team, they have real good depth in the squad, they can do things differently and we have to be prepared for that."