The United boss felt that his side should have had a penalty in the first half when captain Stuart Armstrong went down after apparently being sandwiched between Prince Buaben and Jordan McMillan, and he also felt that McMillan may have merited a red card for a stamp near the start of the second period.
"I think if it's anywhere else he (Collum) gives it," said McNamara of the Armstrong incident.
"It's a free-kick, he's through on goal.
"I was a bit irate with the challenge on young Andy Robertson as well down the side of us. I thought the lad stamped on him and we never even got a free-kick for it."
Farid El Allagui finished off a fine United counter-attack to give the visitors the lead after 27 minutes, but Gary Fraser hit back for Partick with 15 minutes remaining to secure the point that was the least their play had deserved.
The draw leaves United without a win in their last seven matches, and while disappointed not to get back to winning ways, McNamara conceded that his side had not been at their best.
"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 - and then the penalty as well.
"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."
Partick's own winless run now extends to five matches, but manager Alan Archibald was relieved his side got the point their play deserved, even if it still leaves them looking for their first home victory of the league campaign after 13 attempts.
"I thought we more than deserved the draw, I thought our play in the second half merited it," said Archibald.
"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."