Manager Ronny Deila thinks Celtic took a "step in the right direction" after opening their Premiership campaign with a 3-0 win at St Johnstone.
"I am calm but I'm not unbelievably happy as I don't think we performed fantastically - but we are on our way," said the Norwegian.
"I have absorbed a lot and observed the way we played before and how we want to play.
"It takes time, and this what I have been saying all the time."
St Johnstone contained the reigning champions without too much trouble until a defensive error from Steven Anderson allowed Anthony Stokes to open the scoring after 55 minutes.
Nir Biton then converted a penalty after Dave Mackay was sent off for a foul on Derk Boerrigter and Callum McGregor's low shot squirmed underneath St Johnstone goalkeeper Alan Mannus.
"The first 20 minutes of the first half was okay but the last 25 minutes of it wasn't the way I want to see my team," said Deila.
"But in the second half we started to up the intensity and pressure and got more movement. It opened them up more and in the end we got the chances we needed.
"The second half was more like how I want to see my team, but we need to work more on the fitness and pattern and transition to improve. But that will come.
"Tonight wasn't perfect but I know it's going to be very good in a few months."
Goalkeeper Craig Gordon kept a clean sheet on his first competitive outing in more than two years, making a good stop from a Steven MacLean shot in the first half.
"I think he played well," said Deila. "He was calm and read situations in a good way. I was pleased with his performance."
James Forrest returned to the line-up to make his first start in over five months and the winger's display also heartened the new boss.
"He is unbelievably important but he is only at 50% what he can," he said. "He had 20 minutes where he was working the defence and then he stopped doing that.
"If we can get his potential out he has to look at [Arjen] Robben and [Franck] Ribery and how much they run.
"He has played for 60 minutes tonight and 15-20 minutes against Legia so he needs time. But he is a very important player for us."