Moyes' difficult start to his Old Trafford tenure continued on Sunday as the Premier League champions were beaten 3-1 at Stamford Bridge.
United have now suffered seven top-flight defeats and their chances of retaining the title appear to be over with leaders Arsenal 14 points ahead.
Former Everton boss Moyes dismissed talk of a crisis after United's latest setback and the defiant Scotsman is relishing the task of getting the club back on track.
When asked by a journalist at his post-match press conference if he is facing a crisis, Moyes said: "No, that's your word, not my word.
"It's a difficult task but perseverance, we'll keep doing what's right. I thought we've done a lot of good things today, we've got players to come back and this is a project that I know I'm going to improve as it goes along.
"There will be changes as we go along on the journey and I'm looking forward to it, but it's a massive challenge.
"I hoped I'd be in a far better position than this, but I'm not so the challenge is there for me and I think, if you're a football person, it's a great one to have."
Moyes refused to write off his side's chances of winning the title despite the significant gap that has opened up between United and the top three - Arsenal, Manchester City and Chelsea.
He said: "What we won't do is throw the towel in until we can't get there. The job is to try and finish first and we'll keep trying to do that."
The 50-year-old was left frustrated with United's defending as Samuel Eto'o scored a hat-trick to keep Chelsea, who are just two points adrift of Arsenal, firmly in the hunt for the title.
He said: "I thought we played quite well throughout the game, but the game came down to two set-pieces. We didn't defend set-pieces well and that was probably the difference in the game.
"We were terrible at defending the corner kick (for the second goal). We headed it out; we didn't defend it well enough at the second phase and found ourselves 2-0 down at half-time."
To cap a miserable afternoon, United had captain Nemanja Vidic sent off for a foul on Eden Hazard after Javier Hernandez had pulled a goal back.
Moyes felt the defender was unfortunate to be dismissed, but admitted Rafael could have been given his marching orders for a reckless lunge on Gary Cahill, which resulted in the full-back being shown a yellow card late on.
"I thought Vidic was a yellow card, but I've seen Rafa's and I think that could have been a sending off," added Moyes.
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