He also said that Stack talked with him in December and January about targeting Tartaglione in the primary election. Her daughter, state Sen. Tina Tartaglione, supported state Sen. Jay Costa, of Allegheny County. for the position of minority leader in November, a post that Stack also sought.
Despite Stack's suggestions, Enggasser supported Tartaglione, who took 25 percent of Tuesday's vote in his ward while challenger Stephanie Singer won 17 percent.
Stack, leader of the 58th Ward, supported Singer, who took 27 percent of the vote there to Tartaglione's 14 percent.
Singer finished first on Tuesday, followed by incumbent commissioner Anthony Clark. Tartaglione finished third for two spots on the general-election ballot.
"It all comes back to Tina," Enggasser said of the firings.
A man who answered the phone at the home of one of the fired employees, Mary Ann Quartullo, said, "No thank you" and hung up on the Daily News.
The third fired employee, Diane Canning, did not respond to a request for comment.
Stack calls the staff firings part of an office restructuring.
"None of it had anything to do with politics," said Stack, adding that he could not "remember anything specifically" about conversations Enggasser had with him on Tartaglione and the election.
Stack said he supported Singer because he liked her ideas on how to reform the City Commission.
"That's an office that has to be above reproach," he said. "I think it was about time that they had a fresh voice and a new approach and new energy."
Stack also said there was no bad blood between him and the Tartaglione family from his failed bid for the minority leader post.
"We've all moved on from that," Stack said. "I'm really surprised that people are still talking about that."