The Jags showed up well on the big stage once again as they went toe-to-toe with the champions but they ended the first quarter of the SPFL Premiership campaign with another home defeat as Neil Lennon's side extended their lead at the top of the table.
A second half strike from Kris Doolan, after neat work from Kallum Higginbotham and James Craigen, had given Thistle hope that they could upset the Hoops on derby day.
But substitute Amido Balde clinched all three points for the visitors, adding to Georgios Samaras' first-half header, to condemn Thistle to defeat.
Boss Archibald said: "There were a lot of positives. We ran the champions very, very close. I was a lot happier with the second half. I thought in the first half we gave them too much respect.
"That was the champions, they are clinical. When they get their chances, they take them. I think if we play like that against most other teams we will not be far away.
"The effort and commitment was there for everyone to see. We worked hard. I am just disappointed that we never took anything from the game. It was great to get the goal, it gave everybody a lift. We had a couple of chances after that, but we were sloppy in possession and gave the second goal away to Celtic.
"It is something as a manager that frustrates the life out of you, corners and free kicks.
"We told them not to give them away and when we do give them away they have all got a job to do. They didn't do it."
Defeat for Thistle means they are now eighth in the Premiership standings after an encouraging start to the campaign.
Doolan followed up his brace in the victory over Inverness last weekend with a poachers goal against the Hoops, his leveller coming just seconds after he had hit Fraser Forster's bar as the Jags piled on the pressure.
The striker now has five top- flight goals to his credit and Archibald is delighted with his No.9 after the Firhill attack came under criticism in recent weeks.
He said: "I said we were lacking someone who could score 20 goals at this level, someone who was prolific and had done it before.
"Kris is well on his way. He has done well, he is up to five for the season from nine starts, which is good. I said before that he has not been playing badly. He missed a one-on-one against Hibs and, as a striker, the spotlight went on him.
"He reacted brilliantly last week and scored a good goal and a tap in. We are delighted with him. I thought he was very good today, he worked their two centre backs and caused them problems.
"All strikers are confidence players. We believe in him here, we always have. That is why we signed him."