The Anfield outfit needed an injury-time equaliser from Yossi Benayoun to secure an astonishing 4-4 draw at home to Arsenal last night.
While the point was enough for Liverpool to return to the Premier League summit on goal difference from Manchester United, the Old Trafford side have two games in hand and can go top again with a draw at home to Portsmouth this evening.
Fernando Torres scored twice and Benayoun netted another with Andrey Arshavin producing a memorable personal performance to score all four Arsenal goals.
Benitez admitted Liverpool made massive mistakes in gifting Arshavin his quadruple and that his team had spurned an opportunity to further crank up the pressure on United.
But the Anfield manager believes his players cannot afford to throw in the towel in the battle with their bitter North West rivals.
I think it was a big chance gone for us tonight, said Benitez. Beforehand, we were talking about having to win every game and we were really disappointed to concede four goals.
Normally we are not conceding those kind of goals. Were disappointed as we made massive mistakes.
Its difficult to explain. We are talking about different players making mistakes at different moments of the game. We were losing and then winning and still making mistakes.
For me, the most disappointing was the last one. We had a corner and had to control outside our box and it was something wed talk about a lot. We were drawing 3-3 and we still had time. But to score another goal at the end showed the team has a very, very good character.
We were talking about still going until the end and we have to do the same.
We have to keep our confidence that we will have our chances between now and the end of the season.
Unbelievably, last nights epic came only a week after Benitezs side crashed out of the Champions League by the same scoreline at Chelsea.
Liverpool fought back from 1-0, 3-2 and 4-3 behind to ensure they have still only lost two league games this season. And Benitez said: A positive is we scored four goals against Arsenal and another positive was the team was fighting and worked so hard until the end and we know it must be like that until the end of the season.
United were in the driving seat before this game and if they win on Wednesday it will be more and more difficult. But they have to win and they have to play Arsenal.
Of the game, Benitez added: I dont remember Pepe having a save to make. But we conceded four goals, all from mistakes.
The fans from the beginning were supporting us, pushing the team and sometimes you play with a little bit of anxiety and you have some mistakes. But at the end we have to give our thanks to the fans for their backing.
Liverpool co-owners Tom Hicks and George Gillett were both in attendance last night having met with bank officials earlier in the day.
The duo sat side by side in the directors box, leading to suggestions that tensions between the Americans have abated.
Meanwhile, Arsene Wenger has promised Liverpool his Arsenal team will give Manchester United a similarly difficult time when they visit Old Trafford in the Premier League next month.
Dont worry Liverpool, weve got to play at United and we will try to win, so it is still very open, said Wenger.
I give my team credit. It was another great performance tonight, and Liverpool were too so a draw was a fair result.
It was a game played at a frenetic pace with top quality technically. Both teams created many chances.
We are half-happy because we scored four goals and half-unhappy as we conceded four goals.
Arshavin is a great player and great players can play anywhere.