The qualifier, let a big lead over 25th-seeded Madison Keys slip away in a 3-6 7-6 (7-4) 6-2 loss on No. 2 Court on Monday.
Anreeva had looked set to become the youngest player since Anna Kournikova in 1997 to make the quarter-finals here when she led by a set and 4-1.
But Keys fought back and Andreeva was given her first warning by Swedish chair umpire Louise Azemar Engzell after flinging her racket across the grass when she lost the second-set tie-break.
She then appeared to slam her racket to the ground when Keys forced deuce at 2-5 in the deciding set, earning a second warning and an automatic point penalty, which gave her opponent a match point.
Andreeva argued her case, saying: "Do you understand what you are doing? I didn't throw the racket. I slid. It's the wrong decision. I slid and then I fell."
But the decision stood and Keys won the next point to clinch a 3-6 7-6 (7-4) 6-2 victory, with Andreeva heading to the net to briefly shake hands with her opponent but walking straight past the umpire.
The Russian said afterwards: "She's the umpire. She's the one who makes the decision. But, honestly, I didn't have any intention to throw the racket. I slid. I thought that I will fall forward. Maybe it did look like I threw the racket.
"For me, she didn't do a right decision. That's why I didn't want to shake hands with her."
Andreeva, who had feared being defaulted after whacking a ball angrily into the crowd at the French Open, is working through the temperament issue by talking to herself in bed every night.
She has taken encouragement from the way Roger Federer overcame teenage tantrums.
"I knew that Federer was struggling with emotions when he was teenager," she said. "Actually when I was younger, I saw that, 'Well, he was struggling also. I'm not the only one who also struggles'.
Now 28, Keys was once a teenage prodigy, and, asked what advice she would give Andreeva, she said: "I would say ignore everyone, and everything that they say, unless you actually care about their opinion."
