He said: "I do not see this as my most difficult time as a manager. I have worked for 21 years now in the job so I have good memories and bad moments.
"So I try to concentrate only on the next game. Obviously I was really disappointed at the weekend, but we must be positive and prepare for this game correctly.
"I feel the disappointment just like any fan. But I must underline that my commitment to this club is still 100%.
"I will try to change the situation. I will support the players and try to improve things."
"If we want to win trophies, you must not say 'we cannot do this', we must fight to the end.
"As a manager you must support your players if they work really hard. If they do not do that you know what to do at the end of the season.
"But during the season you must support them, work hard with them, and they must compete for positions in the team."
Benitez also does not believe his future depends on winning the Champions League.
He said: "I do not know too many managers who are told they must win the Champions League. If you win it once it is normally good enough, nobody here is saying we must win the European trophy.
"We must be positive, improve and stop the mistakes. We know we are good team and if we win games the confidence will soar again.
"When I came here the club had gone 21 years since they won the European Cup.
"Everyone is disappointed by the cup result against Barnsley, the players, the staff, everyone in the club. But we cannot change anything now.
"We must keep going, thinking about the Champions League and fourth place in the league.
"We must progress as far as we can in Europe and make sure we are fourth, at least.
"We have more determination now to do well in what is left for us this season."