Without a home win since their return to the top flight, Thistle matched the champions for long periods but paid the price for two moments of slackness.
The Jags' defence was posted missing when Georgios Samaras was given the freedom of the penalty box to head the visitors in front shortly after the half-hour mark.
Despite a fine leveller from Kris Doolan, an error from Sean Welsh in midfield led to substitute Amido Balde securing all three points for the unbeaten Hoops.
Archibald said: "Giving away the goals was very, very poor and it's something that we are going to look at.
"We said before the game don't give them set plays as we knew they were a danger but everyone had a job to do and they didn't do it properly.
"Although we didn't take anything from the game I think we deserved at least a point and I will take a lot of positives from it as if we play like that against most sides we will probably win.
"I know Celtic had a few chances in the first half but I thought we were better in the second half... and we won't be playing the champions every week.
"When we receive possession we need to score a second goal I think. We gave them a chance to break and take possession of the ball and that's what champions do."