Trzaskowski, the mayor of Warsaw, congratulated incumbent conservative President Andrzej Duda for securing another five-year term in Sunday's election.
With 99.99 percent of the ballots counted, Duda had 51.08 percent of the vote, while Trzaskowski had 48.92 percent, the National Electoral Commission (PKW) said on Monday.
"Congratulations to Andrzej Duda for winning. Let’s hope this term will really be different," Trzaskowski said.
Poland’s governing conservatives last fall won parliamentary elections for a second consecutive term, and will be able to keep their grip on power by maintaining control of the presidency.
The Polish president has the power to veto legislation passed by parliament, a key prerogative in a country where traditionalists and liberals are bitterly divided.
After polling stations closed on Sunday evening, an exit poll showed a smaller gap between the two presidential candidates.
Trzaskowski told supporters at the time: “We said it would be close and it is close. But I’m absolutely convinced we will win.”
In the first round of voting in the presidential ballot on June 28, no candidate won an outright majority, meaning a second round had to be held.