Baker was left to rue his missed chances as he went down 7-6 (7/5) 7-5 6-2 to Rosol, who found fame last year after beating Rafael Nadal at Wimbledon.
The Glaswegian served for the first two sets but could not get the job done as Rosol's all-or-nothing game clicked at the vital times.
It amounted to a frustrating afternoon for the world number 246.
"I had my chances, served for both sets," he said. "That was the whole gameplan. The way he plays you just try to stick with him, don't let him get a lead and get confident.
"I executed it perfectly until those two games when I didn't take my chances.
"I was playing the right way but it's difficult to analyse that particular match in that he doesn't play like anyone else on tour.
"He's like a freak show. He doesn't put the ball in court the whole set but he continues doing the same thing. Any sane person would change tactics but he doesn't and then sure enough it happens at some point. It's very difficult to get any control."
Baker attempted to take the positives out of a fine week Down Under and the consolation of a £18,100 prize - he revealed his struggle to make a living from the game had also been eased by being handed down a car from his gran - but his mood remained one of regret.
"It's a good achievement winning three matches in a row (in qualifying) but because of the way the match went today I feel very disappointed about not still being on court," he said.
"I could see during the third set that he knew he had got out of jail."