"I congratulated all the players when they came off the pitch and I told them, 'Cheer up, because it would have been much worse had we lost the game'," Smuda said after Friday's match in Warsaw's brand-new National Stadium.
"However 1-1 is not the end of the game. The tournament is still open, so we shouldn't concentrate on this result, we should just focus on the next match and win."
Smuda, who was experiencing his first competitive match with the Poles as they have only had a series of friendlies being the co-hosts, said that the players had felt the pressure of playing at home on such a big stage.
"We were very well prepared we could see that during every training session but we had great pressure and great stress and I think it was a big burden for them unlike the Greeks," said Smuda.
"We're just at the begining and I think the objective of getting through the group we'll achieve it."
Goal scorer Robert Lewandowski was more downcast than in celebratory mood despite his 17th minute header showing the class he has displayed for German champions Borussia Dortmund.
"We didn't achieve the victory so for me it has no meaning if I scored the goal or it was someone else," he said.
"I regret we didn't take advantage of the opportunities we had in the first half."
With Smuda tipping Russia as Group A favourites, the Poles know they will have their work cut out in their next game, which has an extra edge because of centuries of bad blood between the two nations.
"We need to be very focussed, very concentrated, in order not to lose the game," he said.
After that game in Warsaw, Poland wrap up their group against the Czech Republic in the southwestern city of Wroclaw on June 16.
"We're just at the beginning and I think we'll achieve our objective of getting through the group," said Smuda.
The Poles were dealt a blow by the loss of Arsenal goalkeeper Wojciech Szczesny, sent off for bringing down Dimitris Salpingidis in the box, and therefore suspended for the Russia game.
"I don't want to comment on the red card," said Smuda.
But substitute goalkeeper Przemyslaw Tyton, of Dutch club PSV, proved his mettle with his penalty save from Greek captain Giorgos Karagounis.
"At his club, Tyton's been really spectactacular, so we know he can defend against penalties," said Smuda.
Greece had already been reduced to 10 men in the final minutes of the second half, after Sokratis Papastathopoulos picked up a second yellow.
(For more sports news and updates, follow Ahram Online Sports on Twitter: @AO Sports / and facebook AhramOnlineSports)