He said: "Honestly, that's as positive as I've felt after a game for a long time".
Twice the the east London outfit lead against the division's bottom side but on both occasions they were pulled back, as goals from Andrew Ayew and James Collins were cancelled out by Wahbi Khazri - straight from a corner - and Borini.
Fans of the Black Cats could be heard uttering out "We want Moyes out" during the team's 2-2 draw with West Ham on Saturday.
"I don't think they've (the crowd) turned against the manager - not the way I" ve seen other managers being treated, ' he said.
Sunderland are winless in their last eight matches too, although they did end a seven-match goal drought against the Hammers before Fabio Borini's 91st-minute equaliser rescued a point.
He said: "When you're a football manager, if you're not doing well, you expect to be criticised".
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While Collins' glancing header within a minute of the restart was greeted with grim resignation by a crowd barely three quarters of the official attendance of 40,168, Ayew's fifth minute opener had brought the first audible chants against Moyes.
This time four years ago David Moyes was about to succeed Sir Alex Ferguson at Manchester United but today he is struggling to restore his tattered reputation at Sunderland where a significant proportion of supporters want him sacked.
Moyes' side will be targeting an immediate return to the top flight, and they will give the Scottish boss funds to spend.
"Which fans are happy?" No one is happy at the minute because of the position we're in.
"We've got a game in hand - we just have to go to Middlesbrough and win now". We know we have the squad and the team to move up the league and finish as high as we can. I don't think we've ever been in real danger of ever looking like we're getting relegated, so we'll look forward rather than back.
"Behind the scenes, the feeling in the dressing room before the game was good".
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