West Ham's first win since Boxing Day, which was rubber stamped by Carlton Cole's first goal in three months on 67 minutes, has moved them up to 14th in the table - but they are only one point clear of the bottom three.
Despite appreciating the joyous scenes following Diamanti's strike, Zola insisted it was time for everyone to pull together.
"We care about this club and want to be successful. It was a good gesture and I appreciated it. It means we are all going in the same direction and it is vital to do well," the former Chelsea striker added.
"We want the team to succeed. We are in a position we don't like and want to improve it and that's the way I took it. The important thing is that we won the game.
"It is important we win games and win well and that we are a unit. That is the most important message we send to everybody. I am motivated and driven to do well for this team and that is the most important thing."
Sullivan comments 'spurred' West Ham on
Sullivan has expressed concerns with the club's finances and said he feared they could go the way of Newcastle, who were relegated from the Premier League in 2009 after a season of off-field turmoil.
"I can't believe the contracts I've inherited," he told BBC Sport. "The club is in a mess and we all have to pull together. It'll be Armageddon if we go down. It'll be worse than what's gone on at Newcastle."
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