The snake doesn't really talk for most of the conversation, It responds through body movements. Most pets and animals will respond to voices, granted this is incredibly sophisticated for a snake. Although this is Harry's first time at the zoo apart from possibly reading about Snakes in a textbook at school he would have no idea about their capabilities.
Harry stared. Then he looked quickly around to see if anyone was watching. They weren’t. He looked back at the snake and winked, too.
The snake jerked its head toward Uncle Vernon and Dudley, then raised its eyes to the ceiling. It gave Harry a look that said quite plainly:
“I get that all the time.”
“I know,” Harry murmured through the glass, though he wasn’t sure the snake could hear him. “It must be really annoying.”
The snake nodded vigorously.
“Where do you come from, anyway?” Harry asked.
The snake jabbed its tail at a little sign next to the glass. Harry peered at it.
Boa Constrictor, Brazil.
“Was it nice there?”
The boa constrictor jabbed its tail at the sign again and Harry read on: This specimen was bred in the zoo. “Oh, I see — so you’ve never been to Brazil?”
As the snake shook its head
So we see that he has no reason to be really surprised, an animal making physical movements is a lot more believable than an animal speaking. Granted to most of us with knowledge, this snakes responses would be incredibly fascinating. I'm sure Harry is happier to just have someone to talk to for once.
Remember also that he only knows he can speak to snakes he has no idea until CoS that snakes can speak to him so clearly when he hears this:
As the snake slid swiftly past him, Harry could have sworn a low, hissing voice said, “Brazil, here I come.… Thanksss, amigo.”
He didn't quite believe what he had heard, the language used is the same that someone who is unsure of what they have seen or heard would use e.g "I could have sworn I just saw..." he clearly has disbelief in what he heard.
Also it's very likely that Harry was distracted with the commotion of Piers and Dudley's howls of horror.
Harry sat up and gasped; the glass front of the boa constrictor’s tank had vanished.
He seems to be too focused on the whole glass front disappearing than to properly focus on the snake. From this point it's likely his mind had wondered onto other things, like trying not to be punished.