United midfielder Marouane Fellaini and Michael Carrick handed the home side a comfortable 2-0 lead inside 19 minutes at Old Trafford in Sunday’s late kick-off.
The Red Devils ended the affair as a content 11 minutes before half-time after Wayne Rooney capitalised on a mix-up in the Spurs defence before the United striker fired past Hugo Lloris.
Spurs trail fourth-placed United by six points following their loss at United, and former Blackburn Rovers midfielder and BBC Sport pundit Savage rubbished talk of Tottenham securing a place in next season’s Champions League.
Savage told BBC Sport: “Manchester United blew Spurs away with front-foot football. You came into the game thinking Tottenham could get something but they have disappointed.
“I think Spurs are out of the race now. Six points behind United and not playing well. I didn’t think they would get in top four anyway but even more so on that performance.
“I said I think United would finish fifth but after today it is going to go down to the wire.”
Spurs face Newcastle United, Southampton, Manchester City and Everton in their final nine Premier League games of the season.
Tottenham have won seven of their 14 games on the road in the English top-flight this term.
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