Little was speaking after seeing Wrexham's hopes of avoiding relegation take a huge blow when they were beaten 2-1 by Mansfield Town at Field Mill in the basement battle.
Defeat means that rock bottom Wrexham, who are still eight points away from safety and with just seven games left, have a monumental task if they are to secure their Football League status.
And Little, who was appointed manager in November until the end of the season, admitted he would like to see the job through at Wrexham – if given the chance – and improve the club's fortunes.
"Stick with us. It is a great club with great fans," said Little, in a message aimed at supporters.
"You can't walk away from it, nobody does that in life and I'm not going to do it unless people ask me to.
"I would love to get it right here. I would love to see those fans singing about great victories because it is a smashing club.
"I have learnt a lot in this short time and I think the message is stick together and stay strong because that is the only way we can take the club forward, whether it be on Saturday or next season.
"The fans love their club. They are disappointed tonight but they need to stick with the club and I'm sure they will."
Little admitted Wrexham have got an uphill task if they are to avoid the drop but he is looking for his side to at least keep their hopes alive by beating Macclesfield, themselves not out of trouble, at The Racecourse on Saturday.
"There have been a couple of occasions where we have played poorly or we have been off the pace but generally speaking we have had a go," said Little. "That is the one motto we have.
"We will continue to have a go.
"We have got a massive hill ahead of us now. But what do you do? You don't run away or hide.
"We will roll our sleeves up. We have got a game on Saturday we have got to win, and we will take it from there.
"Hopefully we will win in front of our fans and give them something to believe in. We will try our best.
"We all know where we sit, and we know what people up and down the country will say.
"We have got to try our best to prove them wrong. Whether or not we can remains to be seen."
Second from bottom Mansfield kept their hopes of climbing out of trouble alive with victory and Little believes many people will believe Wrexham have blown their chances.
"We are all absolutely gutted at this moment in time and rightly so," said Little.
"It's been a hard journey. It's been hard since I've been here so I can't begin to imagine how some of them feel having been in this for two or three years now.
"I said that most people up and down the country would look at this game and if someone loses it, they would back them to go down.
"And I accept that's what other people will think.
"I will say the same message I have said from day one. We will keep trying very hard.
"We won't give in. We won't accept horrible, miserable faces on Thursday morning with them."
Wrexham were undone after conceding two goals in three minutes in the early stages of the second half, while substitute Marc Williams' late strike proved to be merely a consolation.
The opening Mansfield goal came from a controversial penalty when Gareth Evans was pushed over and adjudged to have handled by referee Nigel Miller.
And Little, who was disappointed with his sides crossing in the match, believes the official may have got the decision wrong.
"I would like to see the penalty decision again," added Little.
"That was obviously the major point of the game, to go 1-0 down early in the second half.
"There were some poor decisions and in a game like this, you need good decisions. The game swayed on a penalty.
"When I look at some of the situations on the pitch, some of the non-fouls that I thought were fouls, for him to give a penalty from there I thought was ludicrous.
"I just didn't genuinely think it was a penalty but if he has got it right then I hold my hands up.
"That changed the whole shape of the game. Then we had a very difficult ten minutes but they scored again in that time, and it is an uphill battle."
Ask Brian
If you have a question for Brian Little email it to digitalnews@nwn.co.uk and we'll ask as many as we can during our next video interview with the Reds boss this Thursday.
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