Niall McGinn curled home a free-kick to level the scores early in the second half, and neither side could find a winner in an entertaining encounter.
"I think the draw was a fair result, but what has annoyed me is that I didn't think it was a free-kick for the second Aberdeen goal," Houston said.
"There were loads of similar incidents in the middle of the park, so I don't understand why Jon Daly standing his ground is a free-kick just because it's on the edge of the box.
"Great credit to the players for coming back from 1-0 down again. I felt we looked dangerous on the counter-attack and worked really hard as a team. There were a lot of star performers out there."
John Souttar became the youngest player in Arabs history after being handed his debut at 16 years and 99 days.
Houston added: "It was forced upon us through injury and suspensions, but I'm never scared to throw young guys in. After the first 10 or 15 minutes he played excellently.
"He looked nervous to begin with, playing a lot of 10-yard passes. One of the things he has in him is a 60-yard pass. He'll be a player for Dundee United as a centre-half one day, I rate him that highly."