It was to prove a familiar story of frustration for the Jags, with the Firhill crowd again left to wonder how their side failed to take all three points from a decent display against John Hughes' side.
Thistle passed up a number of gilt-edged scoring chances in the 0-0 draw as they missed the chance to open up a bigger gap to 10th-placed Ross County in the Premiership standings.
The Jags have not won since seeing off Caley in October and have yet to taste victory on home soil in Scotland's top flight as they gear up for Sunday's visit of Motherwell.
Boss Archibald said: "The positives are that we got a clean sheet and a point from it but I thought we deserved to win the game on the chances we created.
"It is not happening for us. We could do with a sclaff, an own goal, it looks like something like that we need.
"The two chances in the six-yard box were gilt-edged chances.
"I don't know if you can try too hard. We are hitting things too well in front of goal. Things aren't falling for us."
Those who made their way to Firhill for this Boxing Day clash still drunk on festive cheer were quickly sobered up as the Thistles played out a first half that saw both keepers rarely troubled.
It was a feisty affair as the tackles flew in, the hosts usually on the receiving end, but the lack of quality was evident as neither side found their stride in the opening exchanges.
Archibald's side were almost complicit in their own downfall after 17 minutes when Conrad Balatoni's poor passback was intercepted by in-form Highland forward Billy McKay, but his effort was blocked by Scott Fox.
Caley keeper Dean Brill should have had to pick the ball out of his net when Kris Doolan found himself in space and connected with a dinked cross from James Craigen.
The striker, at full stretch, couldn't keep his header down, however, as he put the best chance of the first half over the bar with the goal gaping.
Thankfully for the near-3000 strong Firhill crowd, the action picked up after the break but while it was better to watch, it was proving another frustrating afternoon for Partick.
JUST minutes after the restart, Thistle again passed up a chance to break the deadlock.
Steven Lawless was the culprit this time as his diving header from a Stephen O'Donnell cross went narrowly wide of Brill's left-hand post.
Their next opportunity was even more clear-cut, Kallum Higginbotham adding his name to the unwanted list of Jags villains. With only the keeper to beat, he somehow lifted his shot over from just a couple of yards out after he ghosted in from the left flank.
Archibald's side continued to flock forward at every opportunity but the goal still eluded them.
Craigen fired wide from the edge of the area and Ross Forbes saw a dipping shot saved. Thistle were left to breathe a sigh of relief that Ben Greenhalgh didn't snatch the win for Caley late on.
Archibald said: "We take the positives from it and we said that after last week [against Kilmarnock] as well. We played good stuff against a very good Inverness side.
"The boys aren't too downhearted. We are desperate to win at home and get the monkey off our back. We will take the positives and move on to Motherwell on Sunday."