The 1-0 loss ensured the champions were beaten twice in a row at home in the league for the first time since 2002, after falling to Everton on Wednesday, with Yohan Cabaye scoring the all-important goal.
It leaves United well off the pace in the title race but Moyes remains bullish over his side's chances of success this season.
"I stand firm that we'll be very close (to the title race)," he told BT Sport, before adding that he remains calm on his own position at the club.
"It's the job, when I came here I knew it was never goiung to be easy."
Moyes will consider his side hard done by after Vurnon Anita appeared to use his hand to deny a goal with the scores at 0-0, while Robin van Persie later saw an effort chalked off due to offside.
"(I'm) disappointed with the result," he said.
"There were bits of the game where we needed a bit of luck and that didn't happen.
"We've lacked a little bit of creativity at times. We've lost the two games (Everton and Newcastle) 1-0 and both have perhaps been a bit against the run of play.
"(Manchester) United fans have been great and I think they understand it's about transition. We'll work and try improve and try get better."
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
