The Hoops took the lead in the third qualifying round first leg through Callum McGregor on 17 minutes, but their good work was undone two minutes before the break when Victor Klonaridis fired in a breakaway equaliser.
The visitors were reduced to 10 men in the 57th minute when Konstantinos Galanopoulos picked up two yellow cards in quick succession, but Celtic could not get the winner against well-organised opponents as the game finished 1-1.
"If we had come in having not made the mistake for the goal and won 1-0, I would have been ecstatic with the performance at this stage of the season," Rodgers told Radio Scotland.
"It wasn't to be but the players were outstanding. I thought we really dominated that first period. We gave away a poor goal just before half time but it was just a case of staying calm and getting our game going again. We continued to dominate after they got the man sent off, and the only frustration was we didn't finish off some really good play.
"But I said to the players, we have nothing to fear. We put in a big performance and didn't quite get the result tonight, but it gives us a chance to go out there and get a result. It was always going to be difficult, whatever the result tonight. But after that performance, I think we feel a lot more confident we can do that."
The second leg takes place at the Athens Olympic Stadium on Tuesday, with the winners of the tie facing either Swedish side Malmo or Hungarian outfit MOL Vidi in the playoff round.