I am not 100% convinced that it is true, it could have been a bluff.
For instance, we see here that Kakashi states that Haku is stronger than him ONLY because he one-shotted Zabuza, but we find out later that Zabuza had Haku wait nearby and that Haku was intended to save Zabuza who was about to die anyway.
We know that Kakashi was superior to Zabuza. Before you say this let me remind you that the only reason that Kakashi got caught in the water prison was because Zabuza orginally used a Naruto, Sasuke, Tazuna, and Sakura, who were ALL useless at the time and actually HINDERING Kakashi. With the exception of Tazuna (and probably Sakura), we know that Naruto and Sasuke could solo Zabuza while eating ramen using only their feet in the current time.
Now Haku, at the same point, lost to an initial jinchuuriki form Naruto. Let's say Kakashi back then was able to at least suppress the chakra of Naruto in his two-tailed form. Zabuza should be on par when it comes to that despite obvious differences in Kakashi and Zabuza's strength.
You must be registered for see links
Based on Ninjutsu, I see it like this...
Haku uses Ice Mirrors and Zabuza uses the Hidden Mist jutsu.
Haku can't attack what he can't see, since he isn't a master of silent killing like Zabuza, meaning that Zabuza can escape the ice mirrors undetected. Haku isn't a sensor either, so he relies on his eyes whereas Zabuza has hearing so sensitive that he can pretty much hear your heartbeat.