The Jags looked to be on course for a huge win in the capital when Kris Doolan gave them an early lead only for Terry Butcher's side to snatch a draw with just a few minutes remaining as Sam Stanton levelled for the hosts.
Thistle have now taken five points from their first three post-split fixtures, but could have moved to within touching distance of Premiership safety had they held on in Leith.
Archibald's side return to the capital on Wednesday night to face already relegated Hearts as the battle to avoid the top flight play-off spot gets set to go right down to the wire.
And the Firhill boss knows it was an opportunity missed for Thistle as Hibs denied them at the death for the second time this term.
Archibald said: "As the away side your main concern is obviously not to lose the game but being one up with so little time left on the clock we've really got to be looking to win it here and, to come away with a point, really feels like a defeat.
"There was a point at the end of the first half where Chris Erskine was through on goal and I think from there we should be looking to go two up and kill off the tie, but it wasn't to be. It is a real blow.
"We told the boys at half-time that they would throw everything at us.
"We thought we would be able to use our pace and nick something on the counter attack, and we did create chances, but we just weren't clinical enough and a bit careless with the final pass.
"It's frustrating in the end, we know Hibs are the home team and they're fighting for their lives just like we are but, at the end of the day, we have to be defending better and seeing games out."
Thistle could return to Edinburgh on Wednesday night minus two of their most influential stars as Archibald sweats on the fitness of Doolan and defender Lee Mair.
The former was forced off with a shoulder injury picked up when he opened the scoring after just eight minutes at Easter Road while the latter didn't see out the first half as he was replaced by Gabriel Piccolo.
Archibald said: "We will know more today, thankfully with Doolan it doesn't look like he's dislocated or fractured anything and I think he's just landed on it awkwardly.
"Lee has just caught a sore one on his knee in a challenge after a corner so we'll have to wait and see."