Benitez has endured a testing baptism to his time in the Blues hot-seat and has been jeered by some supporters unhappy with his appointment in the wake of Roberto Di Matteo's sacking.
The former Liverpool boss saw his new charges claim their first Premier League win under his tenure at the fourth attempt against Sunderland on Saturday just days after their Champions League defence was brought to a shuddering halt at the group stage.
The Spaniard has highlighted the relentless schedule of matches since his appointment, with the Sunderland game their fifth in a fortnight, and was keen to pay tribute to the Chelsea fans who have been in touch to offer their support.
Benitez told his personal website: "From the moment I accepted the offer to join Chelsea, my team and I have worked towards improving the results and getting the wins that we all want - no matter what hours we have to put in and the effort and sacrifice in order to achieve this.
"As you can imagine from what you may have seen, we have been immersed in the tasks ahead and since the change in my work situation it has been a cycle of training and matches with virtually no time to do anything else.
"My official presentation as Chelsea manger took place on Thursday November 21 and I came straight from Abu Dhabi where I was giving a lecture. We literally walked straight off the plane into running my first training session in Cobham. After two sessions we faced my first match in charge against Manchester City and then just a further two sessions before facing Fulham in a local derby.
"Two massive league commitments in just three days. We had a couple of conditioning workouts with referrals and then another London derby against West Ham United. We rested on Sunday and then the same timetable again, Nordsjaelland and then Sunderland.
"The team's win against the Danish side (6-1) was the biggest home win of the season for Chelsea but was not enough for us to progress in the competition. The results of previous matches of the group stage and the results that occurred on the night in other games left us without options. We would have liked to be able to offer our fans another ending to this story, to offer our fans another Champions League win but we now look forward to the Europa League.
"We are now challenged with the Club World Championship in Japan and it will not be easy - I tell you this from the experience of two previous participations with differing results. This team is willing to give everything to try and return with a new title to bring home to the fans.
"But let's get back to why I am writing this letter and the basic purpose of trying to give a full account of my new situation and feelings before I seize this exciting new challenge of coaching at Chelsea FC. It is on that basis of the challenge I accepted the offer that was made. With the same faith, the same honesty, with the same loyalty and dedication I put into each of my previous projects.
"That said, thank you all for your support, to those who have sent messages, emails, letters... To those who have called, who have tried to contact by any means possible... To all, I sincerely thank you for your support. We're going to Japan right now to fight for the FIFA Club World Cup spurred on with all of your support."
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