Ahead of a must-win UEFA Champions League clash with Lyon on Wednesday, the Spaniard has come under intense scrutiny following a run of six defeats in seven games.
During that time Benitez's transfer policy has been questioned, while he has also been criticised for a failure to produce significant homegrown talent since succeeding Gerard Houllier in 2004.
But the former Valencia boss remains in a determined mood as an injury-hit Liverpool prepare for their outing in France, where defeat would leave the Reds almost certainly facing elimination from Europe.
Benitez said: "The players are working very hard, they are positive and determined. They know this result is important for the club, for everyone.
"But our fans have not turned. They are clever people, they know the position the club was in when I arrived and they know what position it is in now, they know this is the only way.
Problems"It is important for everyone to see the bigger picture, I am sure things will change in a few weeks when we have our players fit again. When we have our big players available, everything will change.
"I do not accept that we have not signed good players, some may not have settled as quickly, but we are doing a good job.
"This is not the right time to be discussing our signings. But we do have good players, and we have too many injuries.
"We have signed very good players, we have a good team and a good squad."
He added: "Losing would be bad for us, bad for the club, but we will keep going. But we are not thinking that way, we are only thinking of winning.
"In a few weeks these problems will have gone. Key players will be fit."