Bergwijn burst through the defence, beating several United men - including Harry Maguire - before firing in a shot that was too hot to handle for David De Gea.
Keane lambasted De Gea on Sky Sports, stating: "I'm shocked at that goal. I've watched a lot of football over the years, but to give away that goal... I'm fuming watching this game of football.
"I can't believe Manchester United! I can't believe [Luke] Shaw, heading the ball in the air and then running forward.
"I am staggered at Maguire. Staggered that an international player can get done like this.
"And I am sick to death of this goalkeeper. I would be finding him at half-time; there's no getting away from that.
"I would be swinging punches at that guy. This is an established international goalkeeper, I am flabbergasted.
"There's got to be something going on at half-time. If I was Ole, make some changes, get some lads off the pitch, some of them are going through the motions at the moment, not that United have been bad, but you've got to impose your personalities.
"Spurs have been okay, they've been compact, they've been okay.
"Maguire and de Gea, I wouldn't even be letting them on the bus at the end of the match. Get a taxi back to Manchester.
"These are all established internationals. And I know we have to sit here and analyse the game. Analyse it until the cows come home! You do your job!
"We're trying to get in the top four - not the league by the way - just on about getting the top four, God forbid about getting trophies.
"I am disgusted with it - Maguire, de Gea, you should hang your heads in shame. Representing Manchester United and letting people run past you? Get close to people! Move your feet."