Evans were beaten in air conditions by Bruxbi, lost four times and failed to install a break point of their own.
“It was a really difficult situation,” said Evans.
“It’s not easy, but it’s tennis, you have to recover and go back there. It all felt very quick today.”
Brooksbi will face Yo Hambert in Friday’s semi-finals, when French defeated British number four Billy Harris 7-6 (7-4) 6–1 on Thursday.
Harris, which will also be in the next week’s Wimbledon Main Draw, was knocked in the quarter -finals in Eastborn for the second serial year.
Like Evans, Harris match was held at court one, not the center court of the tournament – some Evans described as “disappointing”.
Evans said, “I have questions why no British players were in the center court today.” ,
“British fans come here to see the British players.”