The Red Devils headed into the game on the back of three successive Premier League defeats and with manager Louis van Gaal under intense pressure.
I thought tonight they played very well
United were much improved and came close to taking the lead in the first half when Juan Mata hit the crossbar and Anthony Martial saw his shot rebound off the post.
Chelsea had chances of their own in an entertaining game at Old Trafford, with Nemanja Matic coming closest for the visitors when he blazed over after finding himself through on goal in the second half.
And Scholes believes that United showed many of signs of improvement during Monday’s game.
Speaking on BT Sport after the game, Scholes said: “I think there is encouragement. There was big pressure coming into the game but I thought tonight they played very well.
“OK, they didn’t win the game. I didn’t quite understand Martial going over to the right-hand side for the last 20 minutes as I thought he was giving Ivanovic big problems. And I think in those last 20 minutes that’s where their attacking really stopped. ”
The result left United in sixth place in the Premier League table and five points behind fourth-placed Manchester City.
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