The Spaniard has been barracked by his own fans since taking temporary charge of the Blues but insists their performance against Arsenal on Sunday was well received
Sunday's 2-1 win over Arsenal was only the Blues' third win in eight home games under the Spaniard, who remains unpopular with many supporters after replacing club hero Roberto Di Matteo in November.
But Benitez declared the watching Russian had reacted positively to the result, which saw Chelsea move four points clear of Tottenham in the face for Champions League qualification, with Everton, Arsenal and Liverpool further behind.
"Without giving too many details, [Abramovich] was really pleased with the game," Benitez told the Daily Mirror. "He has ideas. I do too.
"We share ideas. It's fine. We explained to each other what we're trying to do. It's fine."
Chelsea take on Swansea City on Wednesday in the second leg of their Capital One Cup semi-final and must turn around a 2-0 deficit.
Benitez played down expectations for the tie, adding that opposing boss Michael Laudrup has been better able to develop his team in an unpressured mid-table environment.
"When you're managing in the middle of the table it's easy to bring in young players or play a certain style. It's when you’re at the top or the bottom when it's harder to impose your ideas," he insisted.
"We have to perform in every game because we're a top side. I don't think about how much money we've spent; in my time here we're in profit.
"I'll try to get my side to win and progress to the final. I don't think we're favourites. At the moment, I think they are."