Jurgen Klopp says Liverpool proved they are back to being a European powerhouse after an impressive 3-1 win at Bayern Munich put them into the Champions League last eight.
Sadio Mane scored twice at the Allianz Arena to take Liverpool - beaten by Real Madrid in last season's final - through with a 3-1 aggregate win.
"It's a big step to get this club back on the European stage," Liverpool boss Klopp said. "We think that is where this club should be, but let's carry on."
Having missed the goalless first leg at Anfield through suspension, a long pass from Virgil van Dijk led to an excellent first-half goal from Mane.
"His first goal was ridiculous - the calmness with how he finished it off," midfielder James Milner said of Mane's effort.
Van Dijk then headed Liverpool into a 2-1 lead from a Milner corner on 69 minutes after a Joel Matip own goal gave Bayern a first-half equalizer. Mane made sure of Liverpool's place in the quarter-finals by nodding in six minutes from time.
Liverpool's win means they join Tottenham, Manchester City and Manchester United in the quarter-finals, the first clean sweep of English sides reaching the last eight since 2008/09.
"We have good feelings from last year, so hopefully we can carry on and go as far as we can," Milner said.
Barcelona captain Lionel Messi, meanwhile, was showered with praise by his coach Ernesto Valverde and also by losing manager Bruno Genesio after his side's 5-1 win over Lyon.
"He was incredible," Valverde said after Messi led the way with two goals and two assists.
Genesio added: "Messi was in Champions League mode. He's a genius and can do things that nobody else can."
The first leg in Lyon finished goalless.
Messi had seen his record of eight hat-tricks in the tournament equaled by Cristiano Ronaldo a day earlier in Juventus' 3-0 win over Atletico Madrid. He had two chances to complete a treble but chose instead to set up Gerard Pique and Ousmane Dembele. Philippe Coutinho also scored for Barcelona.