Ten Hag frustrated by costly mistake in Man Utd's draw with Twente
Eriksen's 35th-minute blast put United ahead, but the Danish midfielder gifted Twente their second-half equaliser 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 Saturday.
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."
After finishing bottom of their Champions League group with only one win last season, it was another dispiriting start to European action for United.
Ten Hag's spluttering team are back in action against Tottenham at Old Trafford on Sunday.
In the revamped Europa League first stage they next face Porto before a clash with Fenerbahce, managed by their former boss Jose Mourinho.