Edinburgh were denied a ninth consecutive victory at BT Murrayfield as Ulster had to survive a late onslaught with only 13 men after Stuart McCloskey and Franco van der Merwe had seen red and yellow respectively.
Despite trailing 14-10 at half-time, tries from Ruan Pienaar and Darren Cave proved to be enough for the Irish province as they claimed a 20-17 victory and Doak was pleased with the resolve his men showed.
"We made it very difficult for ourselves, but the boys showed some real character," he said.
"We talked before the match about coming away from home and sometimes having to play ugly to win, but that
was a bit too ugly.
"It was great to get a win because we knew that it was going to be a difficult game. Edinburgh have been on a pretty good run."
McCloskey was dismissed on the hour mark for a challenge on Hamish Watson while van der Merwe saw out the last five minutes of the game from the sin bin.
"I thought that we managed the game well until the sending off," Doak added. "We just lacked discipline and that caused us a few problems at the end.
"I am unbelievably happy for the players. They have been working hard and maybe that is the little bit of luck that we needed."
Despite the grit his players showed in victory, Doak conceded his team still had a lot to work on ahead of Friday's home game against Scarlets.
"We just had a couple of lapses in concentration and then they went down the other end and scored a try and suddenly were in the lead," he said.
"That is something that we need to work on - not to give points away so easily.
"For us to come away from home and grind out a win at Murrayfield, when down to 13 men was outstanding."
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