The Young Lions wasted countless chances in an unnecessarily nervy match against Moldova on Thursday evening, as Gareth Southgate oversaw a profligate performance in his first match in charge.
West Brom forward Saido Berahino's early goal looked set to be the first of many, but the England Under-21s failed to kill off the game and Zaha has urged the side to improve in front of goal.
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"We let go of a couple of chances and that might cost us in another game. We dominated it for most of the time and we just needed to take those chances.
"Against Finland we need to carry on the way we played against Moldova because we’ve got some good players. With the team we’ve got we’re good enough to have a decent campaign."
The match against Moldova marked Southgate’s bow in charge of the Young Lions and, with the new boss having called up a number of new faces, Zaha says the team still need to adjust to each other.
"It was my first game with some of these players and we all play differently and just have to understand each other really," the 20-year-old added.
"But for a first performance together, it was a good game for everyone. The squad has gelled together really well, we all get on well and when we get on the pitch we’re just on the same wavelength."