The Blues are 19 points short of Manchester United at the top of the Premier League and have endured disappointing exits from both the Champions League and Capital One Cup this season.
But, after scoring in a 2-0 win over Middlesbrough which sealed the Blues' place in the quarter-finals on Wednesday, Moses underlined the importance of lifting the trophy.
|5/1||Chelsea are 5/1 with William Hill to win the FA Cup this season
The 21-year-old went on to praise his team-mates for their performance during a potentially tricky away tie at the Riverside Stadium.
"It was a great win for us," he added.. "Right from the start we wanted to get the game out of the way.
"They were a good side, they had a few chances as well, but we managed to capitalise on the ones we had and win the game.
"In the first half both sides had chances. We had our own but weren't able to take them and we knew in the second half that if the chances came we'd have to take them.
"It wasn't an easy game and we're delighted to come away with the victory.
"It was great work from Hazard and Oscar [to set-up Moses' goal]. They're both great players as we all know, it was a nice one-two to slip me in and it just needed a little touch from me to put the ball in the back of the net.
"Hazard's a quality player, we see week-in, week-out what he can do, and playing alongside him can only help me."
The west London outfit will meet Manchester United in the last eight but must keep up their challenge for a top-four finish against West Brom at Stamford Bridge on Saturday.
"We've got an important game coming up on Saturday," Moses added. "We're looking forward to it but it's not going to be an easy game, so we need to make sure we get three points."