John Baird's first-half opener had seemingly set the basement boys on course for a shock win but Billy McKay's 83rd-minute header meant they had to settle for a point.
"They gave me everything," Brown said of his players. "We scored a great goal and played some decent football.
"The only disappointing thing was losing the goal at the death as you're always liable for that to happen against a quality side like Inverness.
"But in terms of commitment and endeavour they were second to none.
"We didn't look like a team scrapping at the foot of the table.
"Instead, we looked like a team in the top half of the table. So all credit to my guys for that."