Benitez was appointed as interim manager of Chelsea until the end of the season on Wednesday after the European champions sacked Roberto di Matteo.
Di Matteo was fired after Tuesday's 3-0 defeat by Juventus in Turin left Chelsea facing elimination at the group stage of the Champions League.
Benitez became unpopular amongst Blues fans during six years as Liverpool manager in which he twice denied Chelsea a place in the Champions League final.
Prior to the London club confirming his caretaker role, the chair of the Chelsea Supporters Group, Trizia Fiorellino, told BBC Sport: "Benitez will just not be accepted by Chelsea supporters.
"I don't think Benitez is a good manager, he's been out of work (since leaving Inter Milan) for two years now. If he was any good, why hasn't any other club snapped him up?"
However, Spackman, who also played for Liverpool, said supporters' views could be changed if the Spaniard got Chelsea back on the victory trail, with the club having won just two of its last eight games in all competitions under Italian manager di Matteo.
Benitez brought Fernando Torres to England, where the striker enjoyed a successful spell at Liverpool.
And Spackman said Benitez could be the man to revive the career of his compatriot, who since a £50 million ($80 million) move to Chelsea in January 2011 has managed just 11 Premier League goals in 40 appearances.
"I thought Chelsea's performance last night was poor and it's been a poor run of results," Spackman told the BBC.
"You won't find many Chelsea fans happy with an appointment of an ex-Liverpool manager. Maybe he has been brought in to get the best out of Torres. He is the interim manager but if he does a good job maybe he will get it for longer."
Despite Saturday's 2-1 defeat at West Bromwich Albion, di Matteo's former club, Chelsea are still only four points behind Premier League leaders and reigning champions Manchester City.
And Spackman added: "Benitez has got a great CV and a good record, but the only way he will win the Stamford Bridge crowd over is getting the results.
"Now he has to focus on trying to win the Premier League."
Earlier, Juan Mata became the first current Chelsea player to publicly comment on the exit of di Matteo, the seventh manager sacked by Russian billionaire owner Roman Abramovich since he bought the club in 2003.
"It's been a difficult day," playmaker Mata wrote on his Facebook page. "Roberto di Matteo is no longer our manager.
"I would like to thank him for all this time with us and wish him the best of luck for the future."
Di Matteo, after the sacking of Andre Villas-Boas, led Chelsea to an FA Cup final win over Liverpool and a penalty shoot-out triumph over Bayern Munich in the Champions League final that saw them become the first London club to lift the European Cup.
However, Portuguese manager Villas-Boas, now in charge of Chelsea's top flight London rivals Tottenham Hotspur, insisted the departure of di Matteo, his assistant at Stamford Bridge, was par for the course.
"At Chelsea, I think another sacking is just like any other day at the office," he said.