United equalled their heaviest-ever defeat in a competitive game and worst since 1931 at Anfield after conceding six times in the second period.
"We didn't give up, that's nonsense," said Rashford at a pre-match press conference on Wednesday ahead of United's Europa League last 16, first leg against Real Betis.
"We were unorganised, yes, communication was bad, yes, that's why we conceded the goals.
"But it comes down to the fact that I believe everyone was trying to get back in the game that much we came away from the team's principles in and out of possession."
Bruno Fernandes (28) has been singled out for criticism for his attitude while captaining the side at the weekend.
The Portuguese midfielder has regularly been appointed Ten Hag's skipper this season as club captain Harry Maguire (30) has slipped down the pecking order.
Fernandes frequently chastised his teammates and even pushed one of the referee's assistants in his frustration.
But Ten Hag confirmed he will remain captain when Maguire is not selected.
"I am really happy to have Bruno Fernandes in my team and really happy that Bruno Fernandes, if Harry is not on the pitch, is our captain," said the former Ajax boss.
United had lost just once in 22 games prior to their mauling by Jurgen Klopp's men.
Ten Hag has already ended a six-year wait for silverware by winning the League Cup and United remain in the hunt for two more trophies in the Europa League and FA Cup.
"We have seen the game, we have to reset and bounce back," added Ten Hag.
"We win together, we lost together. We made a mess on Sunday and we have to deal with it."
