"I am just thinking about the next game," Benitez told reporters when asked whether Wednesday's result, which means Liverpool's European fate is out of their hands, could threaten his job.
Nine points behind leaders Chelsea in the Premier League, Liverpool lie third in their Champions League group on four points from four games, six points from leaders Lyon, who have already qualified, and five behind second-placed Fiorentina.
"We are really disappointed because it was a great opportunity for us," said Benitez, whose team had to share the points after conceding a last-gasp goal scored by Argentine striker Lisandro Lopez.
"Clearly it is difficult for us to qualify but not impossible," added the Spaniard, whose team will next visit Debrecen before entertaining Fiorentina.
"We have a chance. The main thing is to play well against Debrecen and then see what the situation is for our last match," Benitez added.
Five-times champions Liverpool travelled to Lyon having lost six of their last seven games in all competitions, including a 2-1 loss to the French side at Anfield, and were again missing injured captain Steven Gerrard.
Benitez also had to make do without Albert Riera, Martin Kelly and Martin Skrtel, among others, while Spain striker Fernando Torres braved the pain from a sore adductor muscle to play.
"I think we had too many problems before the game so I am quite pleased with the performance of the players," said Benitez, whose team created many chances in Lyon but were denied by a superb performance from France keeper Hugo Lloris.
"I think it will be good to analyse the performance of the team," the Liverpool manager added. "The players will see we were working very hard and had many chances and that is positive. The players know that if they work as hard as this, they will win matches."
(Writing by Patrick Vignal in Paris, editing by Justin Palmer)