The Spaniard allowed the Argentine's tame effort from outside the box slip underneath his arms in the European Cup quarter-final second leg at Camp Nou, which gifted Ernesto Valverde's side a 2-0 lead.
Messi opened the scoring after 16 minutes on Tuesday night with a brilliant solo effort, but his second goal four minutes later is destined to go down in history for De Gea's uncharacteristic error.
Barca went on to win the match 3-0 and qualify for the last four of the competition 4-0 on aggregate, with a huge tie against Liverpool now on the horizon.
Speaking to Spanish radio station Cadena COPE, Ter Stegen admitted that he could not celebrate Messi's double because of the empathy he felt for De Gea.
"The truth is that it took me a while to celebrate the goal," he said.
"He plays in the same position as me and so I shared his pain."
The Blaugrana number one also revealed that he consoled De Gea after the final whistle, adding: "I told him that we are all human and the second goal could have happened to me.
"Life goes on."
Ter Stegen had a relatively quiet night against the Red Devils, who struggled to create many clear cut chances, but he did produce one exceptional save to deny Alexis Sanchez late on.
The United substitute headed a pinpoint Diogo Dalot cross goalwards only to be denied in spectacular fashion by the 26-year-old.
Barca have benefitted from Ter Stegen's brilliance between the sticks throughout the 2018-19 campaign and his efforts have not gone unnoticed by the club's president Josep Maria Bartomeu.
"He's good on the line, he has great reflexes, he can handle the ball very well.
"We appreciate him as a human being very much."
Ter Stegen will be back in action for Valverde's side on Saturday as they take in a trip to Real Sociedad in La Liga, with the title all but sewn up heading into the final weeks of the campaign.