"I'm really pleased to get into the semi-final again this year. I'm pleased with the second half and not so happy with the first half," Rodgers told reporters in his post-match press conference.
"It was a very tricky tie for us, especially with the week we've had. I think our lack of training time showed in the first half.
"We weren't up to our standard really in terms of our intensity, pressing and creativity but we also have to give credit to Greenock Morton because they showed good organisation, had some good players in their team an I thought they played really well."
Celtic could face either Rangers, Aberdeen, Motherwell, Kilmarnock, Hearts or Falkirk in the semis.