Procter & Gamble — the company that sells, among others, Tide and Pantene products — is being pushed to be more creative as consumers increasingly prefer more niche brands, the analyst at Consumer Edge Research said.
But P&G CEO David Taylor told CNBC the vote was only motivated by the desire to grow the company.
"It's concern for the future of this company," Taylor said. "The board of directors for Procter & Gamble is extraordinarily committed to not only the short- and mid- but also the long-term success of the company."
Peltz said board members are frightened of what he will bring to the company.
"I threatened the hallowed halls of that boardroom," Peltz told CNBC after the shareholder meeting. "The fact is the board needs refreshment. The board needs to really look honestly and openly, and say, 'What's wrong with this picture?'"
Peltz said he's still waiting for the vote's final results and will fight for a seat regardless. Peltz's company, Trian Partners, has a $3.5 billion stake in Procter & Gamble, which has a market value of $230 billion.
Shares of P&G dropped after the news and were down 0.89 percent in afternoon trading.