Gary Fraser's strike with 15 minutes left to play cancelled out a first-half opener from Dundee United's Farid El Allagui.
And following Fraser's equaliser Archibald thought Thistle were unlucky not to take all three points.
"I thought we more than deserved the draw, I thought our play in the second half merited it," he said.
"I thought we had enough pressure to maybe get the second but things just weren't dropping for us.
"Even before we got the goal it didn't look like we were going to get it as things were falling either side of our strikers.
"I was delighted when we got the goal, and I thought we were going to push on and maybe deservedly nick the winner."
Dundee United boss Jackie McNamara thought Thistle played well in the second half but felt his side should have made sure of the win before the home side managed to equalise.
"I thought Thistle put us under a lot of pressure second half and we stopped passing the ball," McNamara said.
"But I also think that we should have killed it off - Stuart [Armstrong]'s chance - that kills the game off and settles everybody down.
"I thought at times we were maybe a wee bit nervous and were a bit too deep, which made it hard for the forwards to go and press the ball, so it's something we need to work on in getting up the park."