A goal from Diego Tristan after 32 minutes sealed a hard-earned 1-0 victory.
Zola said: "We have never lost focus that we could get into Europe and it remains a possibility. We will try hard until the end. I know the players are very determined to achieve this.
"I know some teams do not want Europe because of the number of games there are. But we have so many young players that to be in Europe would be a big thing for them. They would improve very much.
"To be honest I am quite surprised to be in this position. I was dreaming of doing a good job but I was not expecting to be pushing for Europe. It is going well."
Tristan made the breakthrough with a superb 20-yard free-kick after Abdoulaye Faye's foul on David Di Michele.
It was the 33-year-old Spaniard's third goal for the club and Zola was thrilled with his team's overall performance.
He said: "We played some good stuff in the first half and the goal was an example of that. We knew they would try to come back in the second half but the resilience of my team was amazing.
"We were aware of Stoke's tactics and how they would play. It was a matter of staying alert and we did that."