The weekend stalemate means Capello's wait for a first Chinese Super League (CSL) victory goes on.
The weekend stalemate means Capello's wait for a first Chinese Super League (CSL) victory goes on and Shenhua said that online speculation about the result was tarnishing the club.
Shenhua called on fans to "resist rumours" in a statement. "There is a lot before and after the game about Shenhua and the opponent fixing the result," it added.
"Was this the performance of a team and coach told to lose the game?"
"Recently a few people with ulterior motives fabricated a lot of rumours without basis in fact. They hoped to bring chaos to football and Shenhua," continued the statement, issued on Sunday.
"We solemnly tell Shenhua fans, please fully trust our management, coaching staff and all the players."
"We have set up a special team of lawyers, using a variety of legal means, to investigate the people involved in these rumours."
Suning, who have splashed out on former England coach Capello and Brazilians Ramires and Alex Teixeira, looked set for a badly needed three points when they went ahead through first-half goals by Wu Xi and a Teixeira penalty.
But Shenhua, for whom the oft-injured Argentine striker Tevez was again absent, struck back on 82 minutes with a Giovanni Moreno goal.
The Colombian international then sent his under-pressure coach Gus Poyet wild when he headed in the leveller in the fourth minute of injury time for mid-table Shenhua.
Suning climbed off the foot of the CSL table on goal difference, but Capello has now failed to win in four league games, drawing twice.
"It should have been a game that we won and the result is a real pity," the Italian veteran coach said.
Reigning champions Guangzhou Evergrande remain top of the table by a point despite a second successive CSL defeat, 2-0 at Beijing Guoan.
Second-placed Shanghai SIPG, without the banned Oscar and Hulk, missed the opportunity to go top as they lost 4-2 at Changchun Yatai.