The ex-Pussycat Dolls star was unable to complete the show's final song due to the disruption at Manchester's Palace Theatre on Friday.
Speaking on Instagram, Thornton said she "fought really hard" to finish the show, but it had not been possible.
The theatre said two audience members who refused to sit down and stop singing were removed by security staff.
The theatre had previously asked people not to sing along to the stage adaptation of the 1992 film, which stars Thornton and former Emmerdale and Hollyoaks actor Ayden Callaghan in the roles made famous by Whitney Houston and Kevin Costner.
A representative said staff were "disappointed that the last 10 minutes of the show needed to be cancelled due to disruptive customers refusing to stay seated and spoiling the performance for others".
They praised the work of the venue's security for "dealing with these difficult circumstances in a professional and calm way" and thanked Greater Manchester Police (GMP) "for their assistance".
The force confirmed officers had attended after two people were removed by security staff.
Audience member Karl Bradley told BBC Radio Manchester that some spectators in the higher tier had started a countdown ahead of the finale, which features the classic song I Will Always Love You.
He said they "started to project themselves" by singing along and attempted to hit the song's high notes, but could not "and that's when the chaos began".
He said Thornton's microphone was cut, though the star kept singing, but "eventually the lights cut off as the drama unfolded".
He added that there were "audible gasps" from other audience members and people were "all stood up, looking up".
Speaking on Instagram, Thornton said she was "just very, very sorry that we couldn't finish the show".
"I fought really hard, it feels awful," she said.
"I respect that you paid your money and I am so grateful to everyone who respects the people on stage who want to give you a beautiful show."
Callaghan tweeted that a "few badly behaved individuals ruined it".
He said there had been "disgusting behaviour" and though the cast "wanted to carry on", they were unable to because "it had become a major incident".
He added that he was "really sorry to what was 99.9% a brilliant audience".
GMP said two people were removed by security staff and spoken to by officers at the theatre.
It said "a decision about any further action will be made once the evidence has been reviewed".
The theatre's representative said future performances would "continue as planned".
"We ask that customers are considerate towards the cast, fellow audience members and theatre team so that everyone can enjoy the wonderful entertainment on stage," they added.