The Foxes go to Tottenham in the Barclays Premier League on Saturday still rooted to the bottom of the table.
Pearson's side have been at the foot since November and are seven points from the safety line with 10 games left.
They have won just once in their last nine league games and the boss conceded their form must improve, but still believes they can stay up.
He said: "It's still a big task for us and with the points we have on the board and shift in form we have to achieve there won't be too many people who share my beliefs.
"The players remain very upbeat and 10 games left is still a sizeable chunk and we have to make sure it's a successful 10 games.
"We have to make sure we remain in touch and that our destiny stays in our own hands
That's what we have to try to do
We have 10 games left, six of them at home.
"Our home form has not been what we would have liked but if we get into the latter stages, with four or five games at home, in contact it's something we can be relatively positive about."
The Foxes have drawn a blank in their last two games with nine-goal top scorer Leonardo Ulloa failing to net in his last six outings, since Leicester beat Tottenham 2-1 in the FA Cup in January.
But Pearson insisted they cannot afford to dwell on the past.
"We've not really created enough in some games but we could also rue missed chances and if we wanted to we could bemoan ill fortune with some decisions," he said.
"That's where we are
There's always quite an honest recognition of where we are
For sure we have to get back to being more ruthless in front of goal but we have a belief in the players we have we can make progress."
Dean Hammond (calf) and Anthony Knockaert (personal reasons) are out for the Foxes aiming to avenge a 2-1 home league defeat on Boxing Day.
They will face Harry Kane after the Spurs striker earned his first England senior call-up on Thursday.
Kane spent four months on loan at the King Power - scoring two goals - in 2013 and Pearson believes his selection is deserved.
"It's been, for a lot of people, quite unexpected but he has had a fantastic season so far," he said.
"It's a positive story for English football and he has made incredible progress
He has worked hard on his game and forced his way into the best 11 on the back of European form earlier in the season
I'm pleased for him
He is a likeable young man."
Source : PA
Source: PA