Jurgen Klopp said he had no problem with winning "three dirty points" as Diogo Jota returned to haunt Wolves with the only goal in a 1-0 win at Molineux on Monday.
A wretched run of six successive home league defeats has left Liverpool with an uphill task to qualify for the Champions League next season.
But Klopp's men have now won six of their last seven games away from Anfield.
Victory moved the English champions back up to sixth and within five points of fourth-placed Chelsea.
"It's all about the result," said Klopp. "It was a big fight. We won three dirty points, I am completely fine with that. We need that to get back on track."
A disappointing night for Wolves ended with a bigger concern than just the result as goalkeeper Rui Patricio had to be stretchered off after 15 minutes of treatment for a head injury following a collision with his own player Connor Coady in the closing stages.
However, Wolves boss Nuno Espirito Santo allayed fears over the Portuguese international's health.
"He's OK. He's conscious, he remembers what happens, he's aware, so they tell me he's OK," said Nuno. "He's going to recover, so it's OK."
Wolves have already been badly affected by a serious head injury this season. Their top scorer for the past two seasons, Raul Jimenez, has been out since fracturing his skull against Arsenal in November.
The absence of Jimenez means Nuno's men have missed Jota even more since he joined the English champions for an initial £41 million ($57 million) in September.
Jota has also been missed by Liverpool for much of the past three months due to a knee injury that halted his flying start to life at Anfield.
But the winger is hopeful his return can inspire a strong end to the season to secure Champions League football either via the Premier League or winning Liverpool's seventh European Cup.
"Hopefully this can be a great start of a run towards the end of the season," said Jota.
- Alisson escapes -
Klopp named the same side that bounced back to form with a 2-0 win over RB Leipzig last midweek to reach the quarter-finals of the Champions League.
However, the visitors should have been punished for a slow start as goalkeeper Alisson Becker somehow escaped without conceding a penalty when he crashed into Nelson Semedo after just two minutes.
Sadio Mane missed two big chances at the other end to open the scoring for the visitors, but the Senegalese did have a part to play in the only goal of the game in first-half stoppage time as he exchanged passes with Mohamed Salah before teeing up Jota for a low shot that should have been kept out by Patricio low to his right.
Liverpool's lack of fluency compared to the side that romped to the title last season was even more clear after the break as they were happy to sit on their lead and would have been punished by a more clinical opponent.
Coady headed wide a great chance to score against his former club, while Adama Traore stung the palms of Alisson and Fabio Silva's weak header floated into the grateful Liverpool 'keeper's arms.
But with Jimenez watching on from the stands, even Liverpool's makeshift central defensive pairing of Nat Phillips and Ozan Kabak were not asked serious questions.
Salah had a second goal for Liverpool ruled out for offside five minutes from time. During his attempt to stop the Egyptian, Coady inadvertently caught his goalkeeper.
A lengthy stoppage ensued before the game restarted in the 100th minute and Wolves used a concussion substitute as John Ruddy replaced Patricio.
Despite a nervy finale, Liverpool held out to take advantage of a weekend in which a host of the other contenders for the top four all faltered.