The La Liga champions suffered an incredible 4-0 loss at Anfield and were dumped out of the Champions League at the semi-final stage despite taking a 3-0 first-leg win.
Valverde's team gave up a 4-1 first-leg lead against Roma in the quarter-finals last season, and the manager was in no mood to pass the blame after a second epic collapse in Europe.
"How does it affect my future? I do not know, the truth is that I did not have time to think about many things, but the coach has to take responsibility," he told Movistar Plus.
The Barcelona boss was also stunned by the winning goal from Liverpool, a quick corner netted by Divock Origi as Barcelona's defenders failed to react.
"An incredible goal has taken us out of the tie," he told a post-match news conference.
"When I looked, the ball was already coming in. We were happy with the strategy situations because there they are a great team, but in a surprising play that I did not see, they scored.
"I did not see the play clearly, I guess we were not watching and they were ready.
Braces from Origi and Georginio Wijnaldum each scored twice to see a Liverpool side missing injured pair Mohamed Salah and Roberto Firmino to their win, making the comeback even more stunning for the Premier League side.
Valverde has now claimed back-to-back league titles, but the failures in the Champions League are sure to see the Spanish boss come under a great deal of scrutiny in the coming days.
Asked for his message to the fans, he said: "We are very sorry.
"Everything we do and everything we play is always to please the fans, so that they are proud of the players.
"In this football, what happens is that everyone expects to win always and there are times when we lose.
"When we lose, we have had to do it painfully. We have not lost until now and we are out. In this story, we are all together."