West Ham handed lifetime bans to five individuals who stepped on to London Stadium pitch while an unspecified number of supporters suffered the same fate for hurling verbal abuse and coins at owners David Sullivan and David Gold in the directors box.
"Our last home game against Burnley was one of my toughest days in nearly 20 years at West Ham, and I never want to see scenes like that again. None of us do," Noble told the club's website (www.whufc.com).
"We need everyone to be together and to be behind the team, because positive vibes inspire the players... on the flip side, negativity can affect players' concentration and confidence, as I believe it did in the second half against Burnley."
West Ham supporters are unhappy about the club's move from the Upton Park stadium which was their home from 1904-2016 while a difficult season has added to their frustration.
The London club are 17th in the table with 30 points from as many games and are two points above the drop zone. The defeat by Burnley was their 14th of the campaign.
"This season has not gone how we'd all hoped it would, but I'd ask you to channel your passion to get behind the team, help us get through the season with our Premier League status intact, and we can reassess things in the summer," Noble added.
West Ham host 18th-placed Southampton on Sunday. They also entertain Manchester United, Stoke City, Manchester City and Everton in the next few weeks.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
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