Juan Mata, Oscar, Frank Lampard and John Terry scored the goals as the Blues rallied to overcome a spirited Bees side after half-time and book their passage into the next round of a competition they have won in four of the last six years.
Afterwards, Benitez praised his side's clinical finishing but reiterated that the club's primary ambition is to secure Champions League football next season.
"The priority is to be in the top four, and if we can progress in the cup competitions until the end, then even better," he told reporters. "But I try to concentrate on one game at a time.
"I have a contract until the end of the season. I'm very happy to be here and working with this group of players, and I will try to win every game and see what happens.
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"We knew they would be working hard, and we knew scoring the first goal could be the difference - they would be more open, and we would have more space. It was a question of time.
"They were working very hard in the first half, and we knew it would be hard to keep that intensity up against a team like us.
"We could have scored in the first half, but we're pleased to score four goals and create as many chances as we did."
Mata was once again the difference for the Blues, firing them ahead from range 54 minutes in, and Benitez was eager to pay tribute to the diminutive Spaniard, along with Oscar and Demba Ba.
"Mata is a very important player for us," he admitted. "But I'm also very pleased with Oscar, with Demba Ba for keeping the centre-backs busy.
"We have good players and if they can find each other they can make the difference, and Mata is often the link between them."