The verdict led nearly immediately to protests.
Police officer Betty Shelby was charged with manslaughter for the fatal shooting of Crutcher, an unarmed Black man, in September 2016.
An autopsy showed Mr Crutcher did have PCP in his system, and police said they found a vial of it in his SUV.
Crutcher's family called the verdict a disappointment and the police department "corrupt".
"Terence was not the aggressor; Betty Shelby was the aggressor", she said. "She's ready to get back to her life", defence lawyer Shannon McMurray said.
In a statement after Betty Jo Shelby was acquitted of manslaughter in the death of Terence Crutcher, Fallin said: "Those who disagree with the verdict have the right to express their opinions".
The jury included three African Americans and Time reported that "at least four of the 12 jurors were crying" as they exited the courtroom.
Protesters gathered outside the Tulsa courthouse in the wake of the verdict. "No Racist Police." A smaller group later blocked a major downtown road.
The judge told them they can only announce their verdict in court, not explain it, but said they were free to explain publicly after the trial concluded.
"When is it going to stop - just officer-related shootings? When will the police change policy?" he asked.More news: Michael Carrick "desperate" to win Europa League
Crutcher is one of at least 20 black people in the USA whose deaths after police encounters in recent years have brought national attention and galvanized the Black Lives Matter movement.
Moments before she killed an unarmed man, Betty Shelby had no idea what he may have been reaching for, the Tulsa police officer testified Monday. The shooting led to the departure of the sheriff.
Frank also criticized the Tulsa Fraternal Order of Police, which filed an ethics complaint with the Oklahoma Bar Association against Kunzweiler for allegedly charging Shelby too quickly due to public and political pressure. An affidavit accused her of "becoming emotionally involved to the point that she overreacted".
Tulsa Mayor G.T. Bynum said the verdict does not change the fact that more work needs to be done to address racial disparities.
The policewoman said she fired because he did not obey her commands to lie on the ground and appeared to reach inside his SUV through a partially open window for what she thought was a gun.
Police dashboard and helicopter video show Crutcher walking away from Shelby and her police cruiser with both arms in the air before he was shot.
Shelby's lawyer, Scott Wood, however, claimed Crutcher refused to answer Shelby's questions about his SUV, walked towards the back of the police vehicle with his hands up, and then put his hands back in his pockets.
Shelby told "60 Minutes" she "could very well be dead" if she had waited to find out if Crutcher had a gun. She testified that Crutcher put his hands on the SUV and moved to reach into the vehicle. Her husband, also a Tulsa police officer, sat in the row directly behind the defense table. Shelby said race was not a factor in the shooting.
"I'm feeling that his intent is to do me harm and I keep thinking, 'Don't do this". McMurray said while Crutcher's death is a tragedy, it's not a crime.