Despite going behind to Alan Pardew's side on three separate occasions during the match, Chicharito's 90th minute winner completed a dramatic turnaround at Old Trafford for the hosts.
The win saw them stretch their lead at the top of the league to seven points over local rivals and reigning champions Manchester City following their defeat to Sunderland, and the 70-year-old boss was delighted with the fightback.
"The statement was the performance, never mind where we are at this moment in time," Sir Alex told reporters.
"That was a championship [winning] performance. Once again the players have proved their courage.
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"They never gave in. They were down three times, but they kept making chances and eventually they deserved to win the game."It's only the courage of the team that's got us out of the mire again, and because of the attacking play we've got in the team."
Newcastle's second goal was a controversial one after Jonny Evans turned the ball into his own net under pressure from forward Papiss Cisse from an offside position, with Sir Alex seen berating officials on the touchline in a number of heated verbal exchanges as a result.
He added: "The linesman correctly whistled for offside because Cisse was in an offside position when the cross was made.
"He also pulled Jonny Evans' arm. If that's not interference, then what is? That was the point I was making to Mike Dean."He said it was an own goal, so it didn't matter that the player was offside. But when you see the video replay he is certainly interfering with the play."