A turbulent season has also seen a new chairman arrive, with British Airways boss Broughton appointed by owners George Gillett and Tom Hicks to oversee the sale of the club.
However, Benitez, who has been publicly backed by the new chairman, said: "I have four years of a contract so we will see.
"I was talking about the speculation during the last two or three weeks and I cannot be talking about it all the time.
"I have showed my commitment to the club and the fans in the past. I have four years of contract remaining and we have to keep working as hard as we can. We will try to do our best until the last day. We don't know when the last day is."
As far as I am concerned it is speculation because I am at Fulham
Fulham boss Roy Hodgson on being linked with the Liverpool job
Israel playmaker Benayoun revealed that, despite signing a two-year contract extension last summer, he may be one of those heading out of the club this summer.
"We do not know what changes there will be in the players, the staff so I think it is too early to speak," the 29-year-old said.
"I do not know personally even if I will be here or I will not be here.
"A lot of things can happen, so we have to wait and see."
Benayoun's uncertainty will be a further cause for concern for Benitez, who speaking in his post-match press conference seemed to suggest the blame for the problems Liverpool have experienced stem from Hicks and Gillett's failure to invest heavily in the squad.
"Always in the past two years the manager here has been taking responsibility for everything," he added.
"The reality is that if you compare with other teams in terms of money, power and the option you have in the market, you can analyse carefully and then you have answers.
"The fans are very clever, they know what is going on. It is very clear that things are like this now and still we have to carry on going forward.
"We will prepare for the next game and then start thinking about things for the future.
"The fans want to know but I want to know what is going on next week against Hull."
Benitez rejected any suggestion that the lacklustre post-match lap around Anfield was his farewell to the supporters.
"We have to say thank you to our fans, as always, because they have been very good," he added.
Hodgson grateful for managers' praise
Meanwhile, Fulham boss Roy Hodgson, who has been mentioned as a potential successor for Benitez after guiding the Cottagers to the Europa League final, dismissed speculation linking him with the Anfield hotseat.
Speaking after Fulham beat West Ham 3-2 on Sunday, Hodgson said: "I have got a contract here at Fulham. I am happy with the job I am doing.
"My name is sufficiently strong at the moment to be linked with other jobs and, of course, that is flattering and it is nice to hear. But as far as I am concerned it is speculation because I am at Fulham.
"We all prefer praise to criticism and love to hatred. It would be ludicrous to suggest I am not enjoying people saying and writing nice things about me and the team.
"But I am trying to keep a level head and keep things in perspective."
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