The Dons took an early lead through Scott Vernon, but a Gavin Gunning header and a horrific own-goal from Jamie Langfield put the visitors ahead at the break, before Niall McGinn thundered home a free-kick early in the second half to ensure the sides shared the points.
"I think we had a good chance to get three points today," Brown said "In the first 20 minutes the game could have been out of sight, but we missed some good chances and the conceded some bad goals. You can't do that against Dundee United because they're a good team, and a good away team particularly."
He added: "I was pleased with the overall performance. With four teenagers in the team, I thought we played exceptionally well. If you take away the two goals we conceded, I don't think Dundee United had many more chances in the game."
Langfield's mistake for the second Dundee United goal is not the first error the goalkeeper has made this term, but Brown was keen to deflect criticism away from his number one.
"The second goal was a goalkeeping error, but I don't criticise individuals," he said. "Up at the other end we missed chances we should have put away. It's only fair that if you criticise the defenders, you criticise the forwards as well."
Tangerines manager Houston was left frustrated by the soft free-kick that led to McGinn's leveller, but felt that a share of the spoils was a fair result.
"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," he 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."
Houston handed Aberdeen-born teenager John Souttar his debut for the Arabs, and at 16 years and 99 days, he becomes the youngest player to pull on the Tangerine jersey, taking over a record that had stood since Ian Mitchell made his debut against Hibs in 1962.
"It was forced upon us through injury and suspensions, but I'm never scared to throw young guys in," he said. "After the first 10 or 15 minutes he played excellently. He'll be a player for Dundee United as a centre-half one day, I rate him that highly."