The Reds squandered a one-goal lead to lose 2-1 after extra time in their third-round replay with the Royals.
Liverpool are already out of the Champions League and are 12 points behind Premier League leaders Chelsea.
"Everybody has been talking about me but I'll keep working hard with my team," Benitez told the club's website.
"From the beginning of the season we have been a little bit frustrated but we have to carry on. When you are in the race you need to keep going.
"We are not in the competition [FA Cup] any more. If the critics are fair, then it's OK but it's been the same for three months."
The defeat was Liverpool's 12th of the season and leaves them facing the very real likelihood of finishing the campaign without a trophy for the fourth successive season.
The Reds produced another below-par performance and were deservedly beaten by a committed Reading side.
An own goal from Ryan Bertrand had given Liverpool the lead but an injury-time penalty from Gylfi Sigurdsson and an extra-time header from Shane Long turned the game in Reading's favour.
"It was difficult to take as we were in the 92nd minute and winning the game. Everything then changed," added Benitez, who was also hit by the news that striker Fernando Torres and midfielder Steven Gerrard require scans on the respective knee and hamstring injuries they suffered against the Royals.
"We started the second half better with more control of the game but after this we were making some mistakes and they had chances.
"We played a strong team and we tried to win the game. Sometimes you don't play as well as you can and sometimes the other team plays well." Reading caretaker manager Brian McDermott was understandably delighted with his side's performance and victory, their first at Anfield.
"I thought for the whole 120 minutes we were terrific and I thought we were good value for the victory," he enthused.
"It's fantastic for the football club, it's great for the chairman and everyone associated with the club."
McDermott believes the win was testimony to the preparation that was done ahead of the match.
"We did our work yesterday and the day before, we knew how we wanted to play," he stated.
"We felt before the game we could come and give a performance but that is not what it's all about, it's about winning games."
Reading have endured a torrid campaign so far, in which they have won only six of the 27 matches prior to the victory at Anfield and are two points above the Championship relegation zone.
The club sacked manager Brendan Rodgers in December, which led to McDermott's appointment as caretaker boss.
The 48-year-old, who has also had managerial stints at Slough and Woking, believes he is ready to step into management permanently.
"I've been around the game a long time, I think people forget that," said McDermott.
"I've been in football for 32 years and I think this is my time now. I'm a novice manager in terms of games but I really believe this is my time."
Source: BBC Sport
>> Terms & Conditions