Villa's 2-0 defeat at West Ham on Tuesday night left them rooted to the foot of the Premier League table, 10 points adrift of safety.
But skipper Richards saw enough at Upton Park - where his side had to play for 73 minutes with 10 men after Jordan Ayew was sent off - to suggest Villa are up for the battle.
"We have the fighting spirit," the defender told the club's official website
"We have 14 games now and we will give 100 per cent until the end
"Until it's mathematically impossible, I will not rule us out.
"We know it will be hard
I am a realist too
I think we need three wins on the bounce and then things start to change
"Norwich is next up - a tough game at the weekend - and if we get three points there it will be a nice start.
"A lot of people have said that the players don't care
I think we showed at West Ham that we fight until the end - whether we have 11 or 10 men on the pitch.
"We did that
But unfortunately we didn't get anything out of the game."
Villa had been the better side until Ayew saw red for a needless elbow on Hammers defender Aaron Cresswell.
The 10 men then fought valiantly until Michail Antonio's header broke the deadlock just before the hour mark, and Cheikhou Kouyate's breakaway goal killed Villa off with five minutes remaining.
It was not the most convincing of victories, but it kept West Ham in the hunt for a European place
They remain just a point behind Manchester United in fifth.
Boss Slaven Bilic can add new signing Emmanuel Emenike to his squad when they head to Southampton on Saturday, as well as welcoming back fellow striker Andy Carroll from injury.
"Andy started to train with us on Monday, and he should be in the squad for Southampton if everything goes well," he said.
Source : PA
Source: PA