Page's comments were published in the same week that Facebook announced a new search product, Graph Search, that moves the social network closer to Google+s territory. The interview with the G Googleboss was, however, conducted by Wired magazine last month.
Asked whether competition from Facebook had motivated Google's social products, Page said: "It’s not the way I think about it. We had real issues with how our users shared information, how they expressed their identity, and so on. And, yeah, they’re a company that’s strong in that space. But they’re also doing a really bad job on their products.
"For us to succeed, is it necessary for some other company to fail? No. We’re actually doing something different."
Page said that he was "very happy" with Google+, the search giant's social product. He added: "A lot of it has been copied by out competitors, so I think we're doing a good job."
The 39-year-old chief executive co-founded Google with Sergey Brin in 1998 when the pair were students at Stanford University. In 2001, they hired Eric Schmidt as chief executive. Page took over from Schmidt in April 2011.
In a wide-ranging interview with Wired magazine, Page said he wanted Google to do more than improve incrementally. "Incremental improvement is guaranteed to be obsolete over time," he said. "Especially in technology, where you know there’s going to be non-incremental change."
He said he was "very excited" about the progress of Android, Google's smartphone operating system. Reminded that Steve Jobs, the late founder and chief executive of Apple, had vowed to "go to thermonuclear war" against Android, Page replied: "How well is that working?"
He added: "At the time we bought Android, it was pretty obvious that the existing mobile operating systems were terrible. You couldn’t write software for them. Compare that to what we have now. So I don’t think that betting on Android was that big a stretch.
"You just had to have the conviction to make a long-term investment and to believe that things could be a lot better."
S hane Richmond Telegraph.co.uk