Spanish defensive midfielder Romeu picked up a problem 14 minutes into the match at the Estadio de Balaidos, while Dutch defender Blind was substituted in the second half.
Girona, who had never before qualified for Europe's elite top club competition in their 94-year history, secured a place in the Champions League by finishing third in LaLiga last season, just four years after being promoted to the Spanish top flight.
Michel said his team were not used to the busy schedule.
"That's (injuries) the biggest concern I have about the game," he told reporters.
"We don't have experience of playing every three days. If Romeu is out for several weeks in midfield, we will be left with a weak team. We'll see what the tests tell us.
"We are inexperienced and every day we are looking for solutions to the new reality. The players have raised their voices and Girona cannot manage like the big teams.
"We lose two players? Well, that's the way it is. We have to train as little as possible and analyse a lot from the office."
Despite dropping two points against Celta, Michel was pleased with his side's performance. The draw extended Girona's winless streak to four LaLiga matches.
Having gone toe-to-toe with Spanish giants Real Madrid and Barcelona for much of the last campaign, Girona, who are part-owned by Abu Dhabi's City Football Group, sit 12th in LaLiga on nine points from eight games.
Celta moved to ninth place with 10 points ahead of the remaining weekend fixtures.
"I'm happy because I have the feeling that my team dominated with the ball," Michel said. "We didn't do badly despite the fact that in the first 15 minutes of the second half they put us under pressure.
"I congratulated the Celta coach because I think it was a good game."
