The Dark Blues had captain Gary Irvine sent off just 20 minutes into the derby encounter at Tannadice but nevertheless took the lead through a superb Ryan Conroy strike in the second half. The visitors appeared poised for a famous victory until the final minute when Michael Gardyne popped up to equalise for the hosts.
But Brown said: "To play for 70 minutes with 10 men, we had to defend very well. We knew we were not going to get many opportunities but we scored a fantastic goal. We caught them on the counter-attack and we hoped we would see it out but Dundee United are a good side and we were at their ground."
He added: "I just felt for our players at the end.
"At the sending-off, Gary led with his elbow but he just went to win the header. I cannot fault the referee but I was a defender myself and when you are using your arms for leverage, there is a fine line between dangerous play. I thought the referee had a good game so I cannot complain about it."
United manager Jackie McNamara was relieved to get a late leveller after seeing his side struggle to break down the 10 men of Dundee.
He said: "It's a case of mixed emotions. We didn't do all that well with the 10 men.
"It was hard but we still kept going to get the equaliser. I have to praise the players for that. They never gave up.
"We had enough chances to win but it wasn't to be.
"We're still in the running for the top-six place but we need more wins at home."