Liverpool manager Brendan Rodgers insists his side still have plenty of work ahead to dispose of Hearts and book their place in the Europa League group stages.
An Andy Webster own goal allowed the Barclays Premier League side to claim a narrow victory in last night's play-off first leg at Tynecastle.
But with Hearts producing an impressive display in the Edinburgh clash, Rodgers will be taking nothing for granted in next week's second leg at Anfield.
He said: "We always respect every opponent. We're not that good to be that complacent, to be honest.
"We've got an awful lot of work to do but I was delighted for the players.
"It was great for me to see some of the players who haven't been playing so much, some of our young talent as well.
"All round it was a good win and another clean sheet, which is important.
"It was a tough game. Hearts are an excellent side, they have started the season well and the atmosphere was fantastic.
"It was always going to be a tough game but it's always good to get a win in a European game and we hope to finish it in the second leg."
Andy Carroll was not on the team sheet, despite his presence at Tynecastle, amid speculation he could be set for a return to Newcastle.
But after the 1-0 victory Rodgers revealed the £35million striker missed out through injury and was hopeful he would be fit to face Manchester City on Sunday.
Rodgers said: "Andy was due to start. He had a slight twinge on his hamstring.
"We had a scan on it and it didn't show a tear, just a slight disruption.
"We tried to give him 48 hours, let him travel, and he trained yesterday to see how it was.
"It was still a bit tight and the medics' advice was it was too much of a risk for him to play.
"It was unfortunate because he has worked well and I know he was desperate to play.
"Hopefully missing the game tonight will allow him to recover for the weekend."
Hearts endured a 5-0 thrashing against Tottenham in the Europa League at Tynecastle last season and boss John McGlynn was keen to avoid a repeat of that result.
McGlynn said: "It was always in the back of our minds and it's something you want to guard against.
"You never know when you come up against quality opposition like this, who possibly could open you up.
"We felt we owed it to everyone to put in a performance and I think the fans who came here can be proud of the team."
At the full-time whistle McGlynn believed his side were worth better than the single-goal defeat.
He added: "The players are disappointed. They realise they played well against a really good side. I think we at least deserved a draw.
"Against that calibre of team they can be proud of the performance, if not the result."
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