Robbie Neilson "had no qualms" about Igor Rossi's red card following a two-footed tackle on Hamilton's Darren Lyon at New Douglas Park.
The Hearts head coach felt the dismissal cost his side the chance to win the game, which ended 0-0.
"I didn't speak to [Rossi] at half-time, it's about focusing on the 10 who are still out there," Neilson, whose team hit the woodwork three times, told BBC Scotland.
"That will be dealt with midweek."
Hamilton were also reduced to 10 men late on, after Jesus Garcia Tena's heavy challenge on Arnaud Djoum.
"The players gave everything, that's all you can ask," continued Neilson. "One silly mistake cost us getting three points but the players stuck together.
"Eleven v 11 we played really well. Even at 10 men we kept our shape well and still had good opportunities. Towards the end we probably should have won it, the chances we had.
"Hamilton at home are a hard team to play against. The players have to adapt quickly and I was pleased with how they did in the first 30 minutes, until we got a man sent off.
"So it's a decent point. We're disappointed not to get three, but we have to take the positives from it."
Hearts are still hopeful of overtaking Aberdeen to finish second in the Premiership. For Hamilton, the focus is on staying in the top-flight and manager Martin Canning was pleased with the way his players responded to losing 8-1 at Celtic Park in midweek.
Hearts had the clearer opportunities in the game, with Rossi, Blazej Augustyn and Dario Zanatta all hitting the woodwork, but the home side did create two chances in the second half that were almost converted.
"It's a point gained, albeit we're playing against 10 men for 45 minutes," Canning said.
"It would have been nice to win the game, but when you play against an experienced team that keeps its shape, it's never easy to break 10 men down.
"I thought we controlled the ball a lot and created a couple of opportunities.
"I haven't seen [the red card challenges] back yet. Initially, the first one looked a red, the second one, you never know, it was quick, coming from behind.
"One thing I've never questioned, is the boys' attitude and work-rate. We'll have ups and downs, but the best way to respond is fighting harder the next week. That's what they did."