Searching questions had been asked of the Spaniard after Chelsea took just five points from four Premier League games since he replaced Roberto Di Matteo late last month, but after this 5-1 win thanks to goals from Juan Mata, Branislav Ivanovic, Victor Moses, Eden Hazard and Fernando Torres, the former Liverpool manager could not hide his relief.
Benitez, whose side only returned from Japan on Monday afternoon after losing in the final of the Club World Cup, said: "I'm pleased with the way that we won and pleased because we came back from Japan with jet lag, sleeping too much, players tired and still the performance was fantastic."
He added: "The first half was very good, the second half was amazing. Coming back we needed to see the fitness of the players and we had to decide to change some of them, so to have this reaction, being mentally ready and after working so hard and playing so well, I'm really pleased with them."
Leeds took the lead in the first half through Luciano Becchio, but Mata equalised two minutes into the second period before a devastating four-goal spell in 19 minutes ended any hopes Neil Warnock's side had of adding Chelsea to their list of Premier League scalps, which included Southampton and Everton.
Prompted by the steadying influence of Frank Lampard in midfield, Chelsea set up a semi-final clash with Swansea, but Benitez was reluctant to pick out individuals.
"I don't like to talk about just one player," he said. "We started with Petr (Cech), Victor Moses and Marko Marin - it was difficult for him without playing too many games to come and perform - and the team was tired.
"Oscar was doing very well and (Ryan) Bertrand and the team was so good that I don't think it's fair to talk about just one player.
"If we talk about the second half, we are closer than in other games. The team is improving in every game and still we know we have to balance the squad a little bit just in case as we have a lot of games and need good players in all the positions."
Warnock felt his side had been well worth their half-time lead, and he said: "I'm disappointed because I thought if Tom Lees' header had gone in just before half-time, it would have made it 2-0 and very difficult for them, but overall we made it a difficult night for them and played some good football."