The Red Devils were thumped 6-1 at Old Trafford on Sunday, equalling the club's worst-ever Premier League defeat.
Following an early Bruno Fernandes goal, the match completely shifted in Tottenham's favour, with Spurs firing off six consecutive goals against a hapless United.
The first half saw Spurs score through Tanguy Ndombele, a Son Heung-min brace and Harry Kane.
In the second half, Serge Aurier got on the scoresheet as well before Kane emulated Son by grabbing his second of the game.
Making matters worse was Anthony Martial's first-half dismissal, with the forward handed a red card for putting his hands on Erik Lamela's face.
The defeat will only add to the frustrations of club supporters, with United's lack of new signings this summer already proving a point of contention.
Following the match, Shaw said that the team was left both saddened and embarrassed by their own performance while also admitting that the club is nowhere near where it needs to be.
He told Sky Sports: "It was a lack of concentration and then a mistake, another mistake, another mistake. We switched off. It really hurts.
"Manchester United shouldn't lose in this manner. It really hurts, it's embarrassing and we've let a lot of people down. We've let ourselves down and the staff down.
"Whoever's on the pitch, whatever the scoreline is, the players on the pitch are the ones who have to take the responsibility.
"We get given tactics, responsibilities that players need to do but when you're on the pitch the manager can give advice, but we're on the pitch.
"We need to look in the mirror, we are nowhere near it at the moment. Maybe it's lucky that we've got a break now.
"When we went down to 10 men maybe we gave up, there wasn't that character on the pitch. We were too quiet and naive. There was many mistakes, we need to do more.
"It's embarrassing. I was embarrassed on the pitch. We need a long hard look at ourselves."
Following Sunday's defeat, Manchester United will look to regroup against Newcastle following the international break.