Poroshenko said he felt "no euphoria" following the exit poll results.
"This is a harsh lesson for me and the authorities as a whole. It is a reason to work on our mistakes," he said at his campaign headquarters in Kyiv.
Video of Zelenskyy greeting the first exit poll, which placed him first with around 30 percent support.
More info on the exit polls from our news desk:
The poll conducted by the Kyiv International Institute of Sociology and the Razumkov Center public opinion organization was based on nearly 18,000 responses to questioning at some 400 polling places as of 6 p.m., local time, two hours before the polls closed.
Two other polls had similar figures. A poll by the TV channels Newsone and 112 Ukraine showed Zelenskyy with 30.7 percent, followed by Poroshenko with 18.6 percent, and Tymoshenko with 13.9 percent. A survey by 1+1 TV channel gave Zelenskyy 30.1 percent, Poroshenko with 18.5 percent, and Tymoshenko with 14 percent.
From Chris Miller in Kyiv:
"Yulia Tymoshenko's spokeswoman tells me: 'We will win all the same. We will get second place. Wait for the official results of the central election commission.' All exit polls thus far show Tymoshenko in third place."
From Chris Miller in Kyiv:
"Tymoshenko's campaign is already suggesting it may contest the outcome, saying their exit polling shows her in second place, which would secure a spot in the second-round election."