The reigning European champions had Cristiano Ronaldo back in contention after his post-World Cup hiatus, but even he could not inspire Santos' men.
It was the hosts who generally controlled proceedings in Lisbon, but they failed to break down their stubborn visitors and it marks an underwhelming start to their Group B campaign.
However, Santos thinks a reaction can be expected in another home match on Monday.
Final da partida. Portugal começa a fase de apuramento com um empate. O foco passa já para o jogo com a Sérvia e queremos a vitória na segunda-feira! Vamos!#PORUKR | 0-0 | #TodosPortugal #EURO2020 pic.twitter.com/EaI3VMglRM— Portugal (@selecaoportugal) March 22, 2019
"The team was good, but did not win. We deserved to win," he said. "The players tried, created situations, but we were not able to score.
"This result will not result in any kind of blow, it will give us more strength for the game with Serbia. The players will rest and recover so we can win.
"Overall the team was well. We didn't win, so you can never say that everything is fine, but we had good periods.
"Essentially, we failed to capitalise on the situations that we were able to create. The result is unfair, it doesn't leave us satisfied, but we have to win the next games."
Serbia, Portugal's opponents on Monday, played a friendly against Germany on Wednesday that finished as a 1-1 draw.
In-form Eintracht Frankfurt star Luke Jovic scored for Serbia, but his finish was cancelled out by Leon Goretzka's second-half finish.