The Black Cats remain rooted to the foot of the table following Saturday's 1-0 defeat at Watford.
Next up is a trip to the rejuvenated champions, who have won their last four matches under new manager Craig Shakespeare.
But Moyes says only a win will do as Sunderland attempt to pull off another great escape.
"There's no time to dwell as we must go again on Tuesday - we pick ourselves up and I've told the players that," said boss Moyes
"We wanted a win from one of these two games and we didn't get it, we came close to getting something, but we'll have to try and get it on Tuesday against Leicester now.
"We deserved a point at least at Watford
I thought we stuck at it and we need to make more of our performance next time out."
Moyes will be hoping top scorer Jermain Defoe can shake off a knock in time to face the Foxes.
The England forward was on the end of a heavy challenge early in the second half, and although he completed the full 90 minutes Defoe did not manage a single shot on goal.
Sunderland trailed to Miguel Britos' header but did look sharper following the introduction of Didier Ndong and Wahbi Khazri, the latter for the ineffective Adnan Januzaj who was jeered by the travelling support.
"I was frustrated by the lack of chances we created, that's been a problem for a while for us," added Moyes..
"The subs we made did well, Ndong and Khazri brought something new to the game when they came on.
"At that point we were a goal down and we pushed for an equaliser but it wasn't to be."
Source : PA
Source: PA