Practice sessions at Indian Wells, California, were streamed on the WTA's YouTube channel this week before the tournament begins on Sunday, with microphones capturing a conversation between world number five Pegula and her coach Mark Knowles.
In remarks that later circulated on social media, the American described French Open champion Andreeva as "a diva" and said she "needs to be humbled".
“The girl is super talented, but mentally she’s kind of...," Pegula said during the livestream.
“I like Conchita (Martinez), but I’ve lost a bit of respect for her,” the 32-year-old added, complaining that Andreeva's coach does not keep her in line.
"The WTA takes full responsibility for failing to inform our players and their teams that microphones, in place to give fans a livestream of the players' practice, were active on the courts at the WTA Finals," the governing body said in a statement.
The WTA subsequently removed recordings of Wednesday's practice sessions from YouTube, although clips of the exchange had already been widely shared online.
A representative for Pegula told The Athletic that the American had "absolutely no idea" her conversation was being livestreamed and never expected a private discussion during practice to be made public. The representative added that Pegula had contacted those involved to apologise.
Pegula, a member of the WTA Players' Council, also praised Andreeva in the conversation, describing the world number three as "wonderful" and "smart".
The WTA Finals, being staged at Indian Wells for the first time, run through November 15th.