Alan Pardew's side took the game to the league leaders on their home turf but were unable to keep it tight at the back and eventually succumbed to a 90th-minute winner from Javier Hernandez.
Santon revealed the visitors went into the game with new-found confidence after their win over Queens Park Rangers last weekend and were disappointed not to have taken advantage of it.
He told the club's official website: "We had a really big chance to win this game, but the last 10 minutes were good for Manchester United and they won, while we come back to Newcastle with zero points.
"I think people thought Newcastle would go to Manchester United and come back with zero points, but we really had a chance to win the game.
"We were confident because last week we won against QPR, so when you win, for the next game you always have confidence. You have a winning mentality.
"Today was like that. We came here to get the result, but in the final minutes we were beaten and we are really disappointed because we should have won."
Despite the defeat, Santon insisted that Newcastle could take heart from their performance ahead of another tough away trip on Saturday, against Arsenal at the Emirates Stadium.
The Italian defender said: "It is a really sad day but now we have to think about the next game.
"We are disappointed but I think we can still go into the next game against Arsenal with the mentality to win.
"If we play the same as we did [against United] - especially in the first half - we can win the game.
"We will go with a winning mentality and I think we can win the game."