The LaLiga champions were sent out, after Tuesday’s humiliating 4-0 defeat by Liverpool, despite winning the first leg 3-0.
It was Barca’s second successive dramatic exit from Europe’s elite competition under Valverde, after being knocked out by AS Roma last year after winning a quarter-final first leg 4-1.
“I feel strong, I’m ok and I’m looking forward to taking a step forward, I’m not going to hide behind a wall.
“I’ve spoken to the president and I have always felt supported by him and he has given me his absolute backing. When something like this happens it seems like everything is falling apart but we know what this world is like.
“Everyone thinks you should burn everything to the ground at moments like this but you have to put things back in their place,” Valverde told a news conference, ahead of his side’s league game at home to Getafe on Sunday.