Papastathopoulos was harshly dismissed for a second yellow card just before half-time in the Group A opener and will be banned for one game. Papadopoulos was substituted in the 37th minute.
"We don't know yet what his condition is. But we have many players available... we will find a solution sooner or later," Santos told reporters.
Santos praised his team's improved performance after a shaky opening 45 minutes, and their efforts after they were reduced to 10 men just before half-time.
"In the first 20 minutes we didn't pay too much attention. We knew Poland would go into this game feeling a lot of pressure. We had a strategy for where we wanted to pressure them but we didn't manage it... then we improved," he said.
"We succeeded in keeping up the pressure... we were confident on the pitch, we always thought we could get into the game again, then the players were very good in the second half."
Greece, who had levelled through substitute Dimitris Salpingidis, wasted an opportunity to take the lead after substitute keeper Przemyslaw Tyton saved Giorgos Karagounis's 70th-minute penalty.
"He just missed it. This is football," said Santos.
Salpingidis added: "After missing that penalty where all the pressure was on our player we tried not to lose the game. We managed to do it and now we've got our point."
Karagounis's miss followed another two missed spot-kicks by Greece in their friendly with Armenia at the end of last month, when Giorgos Samaras and Kostas Katsouranis were denied.
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