The defeat saw Ospreys, who had won at leaders Ulster a week previously, slip three points adrift of the top four, and Rees admits it is vital they respond quickly when they welcome Edinburgh to the Liberty Stadium on Friday.
"We've spoken in the dressing room about how tight it is in the top half of the table," he said. "The top six this season are proving very consistent as illustrated by Glasgow.
"It's crucial that we pick up the pieces of this defeat, learn from it and show the right spirit.
"We've got two particularly tough games to come over the next couple of weeks, at home to Edinburgh and then away to Munster.
"Edinburgh is a crucial test of character for this group and we need the support of our fans. It's important that they do their bit to lift this team which is giving everything for the cause."
Rees gave credit to Connacht, and in particular former Scotland international Parks, for their defeat of his side on Friday.
"It was incredibly frustrating," he said.
"Dan Parks played well for Connacht, he was particularly effective into the wind in the second half, putting in some very good kick returns that we struggled to deal with."
"It was one of those evenings when we could and maybe should have done better, but we can't have any complaints about the outcome. They were the better side."
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