But Purslow said Benitez would remain and added: "He is under no threat.
"I'm on the record as saying Rafa's signed a new five-year contract - he's four months into that contract so to discuss that is not appropriate."
Liverpool's slender hopes of qualifying for the knockout stages were dashed by Fiorentina's 1-0 victory over Lyon.
Despite their own 1-0 win in Hungary, the Reds can finish no higher than third in Group E, behind Fiorentina and Lyon, with one round of matches still to go.
Purslow, 45, who took over many of the responsibilities of former Liverpool chief executive Rick Parry in June, sees Benitez's long-term future at Anfield.
"You don't deviate from long-term plans for people and the way to take the club to the next level because of two late goals against Lyon, and that's what it boils down to," he added.
Failure to progress from the group stages left Benitez ruing the late goals conceded against Lyon.
The Reds were beaten 2-1 by the French champions at Anfield before drawing 1-1 at the Stade Gerland.
"It was our own fault in the end, the late goals we have conceded along the way have cost us," conceded Benitez.
"We have been so good in the last few years that maybe people think it is easy to qualify in all competitions.
"We have to be disappointed, we knew we had to win and we did that. You cannot change what happened in Florence but at least we did our job."
The main prize has gone and to be playing in the Europa League is disappointing but we have to accept that, move on and try to win that competition Steven Gerrard Benitez played down the financial significance of his side's failure to progress in the competition.
"You have a budget at the beginning of the season and it assumes that we have qualified for the group stages of the Champions League. We did this," said the Spaniard.
"Two or three more games maybe, in terms of money, won't make such a big difference.
"The main thing for us is to finish in the top four and to be in the Champions League group stages again next year."
Liverpool's win over Debrecen came courtesy of a fourth-minute strike from David Ngog.
But Peru international Juan Vargas scored the all-important goal for Fiorentina, scoring from the penalty spot after 29 minutes at the Stadio Artemio Franchi.
The Reds, Champions League winners in 2005, must now to turn their attentions to the Europa League.
"We'll try to win that," stated Liverpool skipper Steven Gerrard.
PHIL MCNULTY'S BLOG It is a huge blow to the profile and pride of a club that lives off the glamour that Europe's elite competition provides "The main prize has gone and to be playing in the Europa League is disappointing but we have to accept that, move on and try to win that competition.
"The only consolation for us now is if we go on and win the secondary one."
First up, though, is a Premier League encounter with Merseyside rivals Everton at Goodison Park on Sunday.
"I have to be positive because you could see the players working so hard on a very difficult pitch," said Benitez.
"In this situation I think more about the players, the staff and the fans. I am disappointed for everyone. Now we have new targets.
"We are in a very bad position because now we cannot win the Champions League again, so the next game has to be won."