The Roar coach was delighted with his side's performance, but less enamoured with a share of the spoils at the final whistle
A lack of polish to their finishing meant the Roar were unable to take the lead until Nick Fitzgerald's well-taken goal in the 36th minute.
But their joy was short lived, when defender Matthew Jurman - promoted to the starting XI in the place of the suspended Mohamed Adnan - slipped in the area in the 51st minute, pulling down Kim Seung-Yong.
Jurman was sent off and, while Lee Keun-Ho's penalty was saved by Roar goalkeeper Michael Theoklitos, Ulsan leveled soon after through Lee Jae-Sung.
Both sides pushed for a winner, with Besart Berisha presented with the best of Brisbane's chances in the second half. With the Albanian unable to take them, however, the Roar had to settle with their third draw from as many Group F matches.
"I thought we played really well for the whole game," Postecoglou told reporters.
"We deserved to be one-up, but going down the man for the majority of the second half it was always going to be difficult but again we created two or three fantastic opportunities for ourselves.
"… With 10 men we still tried to play our football, we still wanted to get the second goal and we weren't satisfied with just getting a point and full credit to the players for that.
"The frustrating thing was we just couldn't get the reward that I thought we deserved."
Meanwhile, Ulsan boss Kim Ho-Gon admitted the draw hadn't helped his situation, as it left them on five points in Group F, equal with FC Tokyo, while Brisbane and Beijing Guoan are on two points each.
Kim had been hoping a positive result would have enabled his side to focus on the league during April which is set to be a busy month for the club.
"Today was the most important game in the group stages. We were going to decide which competition to concentrate (K-League or ACL) after today's result but we got an unwanted result," he said.
He added: "Other team's results aren't important. We will try our best in the remaining games. We have a busy schedule, playing three games a week and we tried to save our energy by winning today, but I am very frustrated."