On-loan Everton goalkeeper John Ruddy played a crucial role in securing Motherwell's sixth clean sheet in seven SPL games under Brown with a succession of saves, mainly from Simon Mensing, early in the second half on Saturday.
But Well could have snatched all three points when John Sutton blazed over after beating the offside trap midway through the second half and Brown admitted fatigue played a huge factor following their midweek draw against Rangers.
However, he warned they will have to perform far better against Hibernian at Fir Park on Saturday.
"It's a bit humbling, we got good praise in midweek and probably deserved praise but we don't deserve praise today," Brown said.
"I'm sure John Hughes, who was here, will be thinking 'We'll get three points against Motherwell'. We have got to prove otherwise.
"We have got an unbeaten run but we're not proud of the two Hamilton performances."
Winger Jim O'Brien agreed that their exertions against Rangers had taken their toll.
"We put a lot into the game on Wednesday and felt bad we never won the game," the 22-year-old said.
"We were confident we could put on another performance but there were too many who weren't at the races, including myself."
The winger was substituted in the 55th minute and Brown said: "He ran himself to an absolute standstill in midweek. We had to prop him up to get him to play.
"Maybe in hindsight we should have freshened the team up and made a few changes because we have got a number of bright young boys on the bench."
Although Hamilton had slightly more chances than their visitors, they also failed to match their midweek display when they won 2-0 at Dundee United.
Manager Billy Reid said: "We went away from home on Wednesday and were brilliant and we came back home and stuttered a bit, but it's another clean sheet and a point on the board.
"But we have got big, big players to come back. Our two most influential midfield players, James Wesolowski and Alex Neil, have to come back and our top scorer (Mickael-Antoine Curier) is not playing.
"But we are fairly happy with the players we've got, Dougie Imrie came in and worked really hard again, and we'll move on."