Grant, who made 11 changes and left skipper John Terry and Frank Lampard on the substitute's bench, was disappointed with his side's display, while at the same time expressing satisfaction with the result.
When asked if it was their worst European performance since he took charge in September, the Israeli said: "Yes, it is a game in which we played less well.
"I am pleased with the result. A draw away from home is good. But the performance could have been better. We didn't create many chances.
"But Olympiacos are a very well organised team and it is not easy to play against them.
"We hope to improve in the return leg."
Grant was clearly rocked by Chelsea's inability to break down a relatively unadventurous side that offered little in attack.
Olympiacos coach Panagiotis Lemonis was happy enough with the result and insisted he would not be changing his style for the return leg at Stamford Bridge in a fortnight's time.
Lemonis said: "We always knew it would be difficult for us once we got through from the group stages but we found Chelsea very strong in defence.
"We will go to London and try to do the best we can but we know it will not be easy against a team with such quality."