Leroy Fer's early close-range finish put the hosts ahead at the Liberty Stadium, but Roberto Firmino's header and James Milner's 84th-minute penalty turned things around after the break as the Reds ran out 2-1 winners.
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Premier League: Francesco Guidolin on Swansea future
Francesco Guidolin concedes he may lose his job after Swansea City fell to another defeat despite taking the lead against Liverpool on Saturday.
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Guidolin, whose side have not won in the Premier League since the opening day, could not rule out the idea that the game would be his last at the helm.
"I don't know, this is not my decision," said the Italian when asked about his future.
"I have just to work every day, every week to prepare the team. This is my job, I know the situation.
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"It's a possibility [being sacked], but the most important thing is to work with passion and to try to prepare for the next game, and games in general, with my style."
Swansea were on top in the first half and worthy of their lead at the interval, with Guidolin unsurprised by their positive attitude.
"They [the players] gave me a good answer, but I was sure of this because our relationship is good," he added.
"[There is] no problem between me and my players. There is a very, very good relationship. I was sure they would play a good game."
The Swans missed a glorious chance to snatch a late point when Mike van der Hoorn somehow steered wide from just a few yards, but Guidolin preferred to focus on the positives.
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"In the first half we played very good football, aggressive, dynamic and had good ball possession against a very strong team," said the 60-year-old.
"This is important for a manager because I can say our team is a good team, but not in a good moment. But we have all the possibility to change the situation."
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