Rafael Benitez breathed a huge sigh of relief after Liverpool dug deep to beat 10-man Bolton 3-2 and get their Premier League season back on track.
Steven Gerrard scored the decisive goal in the 83rd minute on Saturday after Glen Johnson, then Fernando Torres had dragged Liverpool to 2-2.
Kevin Davies and Tamir Cohen scored Bolton's goals, the club's first league strikes of the season.
After losing to Tottenham and Aston Villa in their first three matches, Liverpool couldn't afford to drop points at the Reebok Stadium and Benitez insisted the victory proved his team have the ability to challenge for the title.
"We showed that we have quality and when they play at that level, they can beat anyone," Benitez said.
"It was a difficult game, twice we had to come from behind but I think that was very positive. They showed character and they showed quality."
The turning point was referee Alan Wiley's decision to send off Sean Davis for a second yellow card after a 55th-minute foul on Lucas Leiva.
Bolton manager Gary Megson was furious and criticised the Liverpool player for making the most of minimal contact.
"There's not a lot you can do, when you're chasing against someone who's got away and he slows up," Megson said. "We've either got to accept it or we've got to start copying it and getting better at chucking ourselves all over the field.
"You control the ball, you wait for the hit from the back and over you go and the referee gets sucked into giving it. We're not clever like that, we never slow down for the hit and then over we go."
Megson also said he didn't believe referees had a good understanding of gamesmanship tactics.
"Footballers know what's going on," he said. "But the knowledge of what's going on, in my opinion is not there (for referees)."
Unsurprisingly, Benitez said Davis's dismissal was appropriate.
"When is a foul from behind, it was yellow card. For me, it was clear," he said.
Benitez preferred to look at the positives after a rocky start to the season. After Liverpool lost two of their first three games - the same total as all of last season - Benitez had criticised his players' lacklustre form.
But the Spanish coach, bidding to lead Liverpool to their first title since 1990, got the response he wanted.
"It was the perfect response from the players," he said. "All the players wanted to impress, they wanted to do well.
"You could see all the players, from the first minute we play, with a lot of determination to win. It's important to have this mentality."
Benitez hopes the forthcoming international break will sharpen his players' match fitness even further.
"We have to improve in other things but at least we have won and the people will be more calm and we can prepare for the next game a little bit more relaxed," he said.
Megson praised Fabrice Muamba's man marking of Gerrard, but said the sending off changed the England midfielder's influence on the game.
"As soon as Sean got sent off, he (Gerrard) got deeper and deeper and just orchestrated everything from there," he said. "It made life very difficult for us."