Ronny Delia admits his side should have been more accomplished in attack despite beating Raith Rovers.
Goals from Kris Commons and Stefan Johansen sealed their passage in the League Cup, although the latter only came three minutes from the end.
Deila praised Raith's performance but also said his own side should have been better in attack.
"We should have more penetration and movement in the last third of the pitch," Deila said.
"But we had two or three very big chances in the second half that we should have finished off. That's these games and I've had more trouble than tonight.
"It was up and down. We kept them under pressure for 90 minutes but we didn't create as many chances as we did on Sunday [in the 6-0 defeat of Dundee].
"It was more flat. We also have to give credit to them, they worked really hard in defence and when you're only 1-0 up everything can happen, so it was very good to get that second goal.
"We deserved to win and we did the job.
"You can see Aberdeen lost [against Hibernian] and other teams as well, so it's good that we're through and three games to a title."
Deila made six changes to the starting line up from Sunday's win, including bringing in 18-year-old left-back Kieran Tierney. The defender impressed, along with Saidy Janko and Callum McGregor.
"[Tierney] has come a long way in a short age, 18 years old to perform like that. He will be important for us in the future," said Deila.
The Celtic manager also said that no decision has yet been made on trialist Carlton Cole, with the former Chelsea and West Ham striker continuing to train with the club.
Croatian Jozo Simunovic sat out the second game in a row but Deila added that the defender's injury is not serious and he could be back in time to face Hearts on Saturday.
"He's twisted his ankle," Deila said. "He's getting better every day, it's not big, but he was not 100% tonight."