Liverpool ended a six-game losing run at Anfield in the league ahead of Wednesday's Champions League clash with Real Madrid.
Jürgen Klopp feared Liverpool were living the "same old story" against Aston Villa, but hopes his side's response to falling behind can help them against Real Madrid in the Champions League.
Liverpool overcome Villa, next up Madrid
The Reds finally recorded a first home win in the Premier League in 2021, though the champions had to rally from a goal down at half-time following Ollie Watkins' opener at Anfield.
Mohamed Salah drew Liverpool level before Trent Alexander-Arnold struck a superb stoppage-time winner, the full-back's goal coming with England manager Gareth Southgate watching on inside the stadium.
Klopp was particularly pleased with the spirit shown by his players, with Liverpool ending a six-game losing streak at Anfield in the league. The 2-1 triumph aids their hopes of a top-four finish this season, while it also offers a timely boost ahead of hosting Madrid in midweek.
"Obviously, the other game [against Arsenal] was really, really good, but today seemed to be the same old story, if you like," the Liverpool boss said.
"We played well but we made one mistake – which is not the biggest mistake in the world – to give them the opportunity to score, and they do. We score an equaliser, which was a great goal – a great pass, great link-up play, all these kinds of things – and then you get the information it is offside.
"We go in at half-time and it's a little bit like the same story again. But it was decided long ago and we have accepted that it’s going to be a bumpy season for us, we have to strike back again, and again, and again.
"The boys did. It took a while until we scored, but we scored a really nice goal. Then, in our situation, we had to increase a little bit the risk, took off a centre-back [Ozan Kabak] for [Xherdan] Shaqiri.
"Then we scored this wonderful goal for 2-1. It was the best goal for ages, emotionally. I'm really happy for the three points."
Liverpool ended an eight-match winless run in the Premier League at their own ground. In doing so, they scored as many goals against Villa as they did across that shocking streak.
Klopp said in his media conference: "It's no secret that it's quite a bumpy season for us. We have to fight through and if, in the end, we finish in a Champions League spot, then great.
"But it's tricky. I'm not surprised any more when things like the first half happen, I'm interested in the reaction. I liked the reaction. If we didn't turn the situation around previously, that's why we lost six games in a row at home, which should not happen - but it happened."
Next up is the return fixture in the quarter-final tie with Madrid, who triumphed 3-1 in the opening leg on Spanish soil.
While making clear his players will give it their all in attempting to turn the situation around, Klopp appreciates they face a tall order against opponents who were so clinical in the first meeting.
"We need a perfect performance on Wednesday if we want to have a chance – just a chance," Klopp said.
"I really think that with the way we played – and the way Real Madrid played there – it doesn't look very promising, but the good thing is we can play better.
"Real Madrid doesn't come here and think they are already through. It's going to be a tough one, but we will give it a try, I can promise.
"This helps, of course. When you are in the moment and win everything, you don't feel the intensity, you just want to play the next game – you would play the next day if you could.
"Obviously, for us in the moment, it's not that easy. We have to work really hard. We have to create five chances to score a goal, or 10 to score. You have go through that, you cannot change it just because you want to. You have to work for it. We did that against a strong opponent, a very important three points.
"Whatever it gives us for Wednesday, we will use."