The win puts West Ham up to seventh in the Premier League table, with Wigan playing on Sunday, and the Hammers are now just four points shy of the designated Europa League positions.
However, Manchester United's capture of the Carling Cup has opened the door for extra places in Europe next term, and Zola insists he will do his upmost to achieve this goal.
"We know that seventh position is possible for Europe, we are trying everything possible to achieve that," Zola told Sky Sports.
"When you have a team that have the team spirit we have it is possible so we're going to try until the end."
The win was secured by two of West Ham's youth Academy products, with goals from 19-year-old Junior Stanislas and 20-year-old James Tomkins, and Zola was impressed by the duo.
"Both of them actually did very well. We knew about Tomkins, he's been playing for a while, playing very well. We didn't yet know about Junior's standards, not only did he score the first goal he played very, very well."
There was some bad news for Zola however, with Jonathan Spector increasing the injury list at Upton Park. The American was stretchered off in the second half after eight minutes of treatment on the field following an aerial challenge.
"I think he's (Spector) got a knock on his head and he lost a little bit of consciousness, he's been taken to hospital and we're just waiting for more news," said Zola.
"It was a difficult game, there were so many players who were playing in different positions from normal. The performance was very, very good. I am very pleased and proud of the team," he added.