Ranked 217, Yuki fought well before losing 5-7 3-6 in the opening round against his Dutch rival, ranked as high as 56.
However, Prakash Amritraj has entered the singles main draw after winning his final qualifying round.
Amritraj came from a set down to edge past Briton James Ward 5-7 6-4 6-4 in two hours and 23 minutes.
Playing under humid conditions, Yuki fought tooth and nail in the first set but made a crucial double fault in the 12th game to give one-set advantage to his rival.
In the second set also Yuki played extremely well as he the returns so well but the experienced Haase was equal to the task.
Haase led 4-3 and then shifted gear to bring in his forehand shots in to play to gain four game points to break Yuki in the eighth game, which was enough for the Dutch to hold his serve to win the match.
Yuki had four break chances in the match but could convert none.
"I had few chances in both the sets but could not succeed. Quite a few opportunities to break his service games. Those few points made the difference," Yuki said after the match.
"It was humid and it takes a toll. I had succeeded in staying with Robin in both the sets. But, Robin stepped up. I feel if I get lot more such chances to play against top 50 players, my progress will be upped," he said. More
