Manager Felix Magath rued Shandong's missed chances, saying: "We didn't create enough good opportunities, especially in the first half, we were the better side but we were also unlucky.
"In the second half, we did much better and put lots of pressure on our opponents and created lots of chances. Unfortunately, out of so many chances we only scored one. I have to say we lost two points today."
R&F retained pole position in the standings as Dragan Stojkovic's team defeated struggling Jiangsu Suning 2-1 on Friday to continue their unbeaten start to the season with 16 points from their opening six games.
Israel international Eran Zahavi scored twice in 15 second-half minutes to cancel out Alex Teixeira's opener for Jiangsu as R&F ended the weekend three points clear.
"If we continue doing what we are doing now, everything is possible," said Stojkovic.
"Jiangsu are a strong team with expensive players so I hoped my players would go in without any pressure and enjoy the game."
SIPG inflicted the first defeat of the season on Manuel Pellegrini's Hebei CFFC with a 3-0 win at Shanghai Stadium to move into second while Beijing Guoan and Tianjin Quanjian drew 1-1.
Guangzhou Evergrande picked up their second win in a row as goals from Gao Lin and Ricardo Goulart saw off Liaoning Whowin despite Wang Shangyuan's sending-off with a quarter of the game remaining for Luiz Felipe Scolari's side, who are now in third.
Tianjin Teda ran out comfortable 3-1 winners over Yanbian Funde while Fredy Guarin and Obafemi Martins scored against Guizhou Zhicheng as Shanghai Shenhua shook off the absence of Carlos Tevez to pick up a 2-1 win.
Changchun Yatai moved off the bottom of the standings when Tan Long scored the only goal of their 1-0 win over Henan Jianye.
(Reporting by Michael Church in Hong Kong; Editing by Clare Fallon)
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