Page made statements against the government during an on-stage question and answer session at a TED gathering in Vancouver, Canada, on Wednesday.
On the previous day, Google founder Sergey Brin had a virtual encounter with National Security Agency whistleblower Edward Snowden on Tuesday.
"It is tremendously disappointing that the government sort of secretly did all this stuff and didn't tell us," Page said during the chat with interviewer Charlie Rose.
"We need to have a debate about that or we can't have a functioning democracy; it is just not possible," Page said. "It is sad that Google is in the position of protecting you and our users from the government doing secret things nobody knows about. It doesn't make any sense."
He also warned that the backlash to online spying and fears over privacy would result in blocking uses of personal information for beneficial purposes.
"What I am worried about is we throw out the baby with the bath water," Page said.
Facebook founder slams the spying programme
Facebook CEO Mark Zuckerberg too, had strongly criticized Washington for its massive spying and hacking programs.
Zuckerberg accused the US government of undermining public confidence in the Internet with its vast surveillance activities.
Documents released last year by Snowden revealed that the NSA systematically spies on phone calls and online activities of millions of people worldwide.