Olivier Ntcham's first-half goal proved decisive as Kris Doolan headed over a glorious chance before Nir Bitton appeared to clip Miles Storey late on.
"It's a foul anywhere else on the pitch," said Archibald. "It's a big call in the last minute against Celtic.
"You don't often get them. We had one in midweek, we usually get one a year so we're not getting two in four days."
Celtic dominated possession but lacked a finishing touch with Leigh Griffiths starting on the bench and Moussa Dembele still missing.
Despite debuts for Conor Sammon and Miles Storey, signed from Hearts - on loan - and Aberdeen respectively, Thistle carried little threat until a late rally.
"We had one good chance [Doolan's] and the late penalty shout," Archibald told BBC Scotland. "We worked ever so hard, it's not easy to contain them.
"I know it's frustrating for our fans that we didn't come out and have a real go but you saw at the end there when we went with two strikers and they can quickly turn you over."
Celtic manager Brendan Rodgers believes referee Andrew Dallas was in a good position to make the penalty call, and felt his side deserved to claim all three points.
"I'd need to see it again," said Rodgers. "It looked from where I was that Nir (Bitton) got a toe to it, and he was the right side of the defender.
"The pitch was maybe a bit slippy at that stage which is perhaps why the boy went down, but the ref was in a great position and he didn't give it.
"We will play better, of course - we were outstanding in the week [the 5-0 win over Kilmarnock] - but tonight is a game we will look back on at the end of the season and hopefully say it was an important three points.
"We could have been more comfortable in the game if we had put our chances away, but when it is still 1-0 you have to defend, and I thought the players were comfortable even though there was bit of pressure around our 18-yard box.
"We didn't quite perform as well as I would want - our standards are much higher than we showed - but it shows the resilience and mentality in the team to get the result tonight.
"That's maybe one of the games we would have drawn last season. So it's good the players can now see out games."
Rodgers revealed he could sign a new striker before the Champions League play-off first-leg tie against Astana on Wednesday.
Griffiths could only start as a substitute due to ongoing calf concerns, while French striker Dembele is out until September with a knee injury.
The Celtic manager said: "James (Forrest) is doing great playing in there, Tom Rogic has played up there and done brilliant for us but the dynamic of the team is better when you have a number nine who can play the role.
"It is really about the availability of a player.
"We will look to bring in quality if available. Maybe (next week). It is something that we have been working towards in the last few weeks, so there may be something happening."
Partick Thistle boss Alan Archibald felt his side should have been given a penalty in their 1-0 defeat by Celtic.