Eriksen broke the deadlock with a powerful shot in the 35th minute, giving United the lead. However, a costly mistake from the Danish midfielder allowed Twente to equalize in the second half at Old Trafford.
Sam Lammers dispossessed Eriksen, who had made a risky turn under pressure, and fired past Andre Onana in the 68th minute.
United manager Ten Hag refused to single out Eriksen, instead insisting the whole team had to take responsibility for their failure to hold onto the lead.
“We kept them alive, 1-0 up, controlling the game you have to be consistent and keep going. In the second half we dropped the level, gave the goal away,” Ten Hag said.
“We didn’t finish it off, we had to go for the second goal and so they stay alive and we get punished with a mistake from ourselves.”
Pressed on Eriksen’s blunder, Ten Hag added: “The goal it’s (a) team (mistake), a player of Twente can dribble through the pitch without stopping. We can’t give a goal away like this.
“We have seen again you have to keep going for the whole game, once 1-0 up you have to keep going, go for the second. It’s the first game, it’s very important you get a win.”
Ten Hag spent a combined 23 years at Twente across three stints as a player and then in different coaching capacities, saying on the eve of the game: “It’s not nice to have to hurt something you love.”
Instead, it was the Eredivisie side who inflicted the discomfort, with a helping hand from another inconsistent United performance hot on the heels of their disappointing goalless draw at Crystal Palace on Sept 21.
Eriksen questioned whether United played with enough desire after their poor run in European competitions extended to one win in nine games.
“I think mostly disappointed as a team, we wanted more in the end, far from good enough. They looked like they wanted it more, that can’t be right,” Eriksen said.
“I think everyone is looking at themselves, everyone is a professional footballer, they know what to do, what can’t happen. We don’t lose but it feels like a loss.”