Albion announced on Tuesday that head coach James Shanahan had left the relegation-threatened club.
Shanahan was released early from his contract, which was due to end in April, after the team lost 27-16 at the Cornish Pirates on Sunday.
That defeat has left Albion seven points adrift at the foot of the Championship table with just three matches to play.
If Plymouth don’t beat Bristol at Brickfields on April 11 then they could be relegated, if second-from-bottom Moseley were to win at Bedford on the same day.
Albion’s chances of staying up are slim, but Dawe said the players and everyone at the club just have to believe it is possible.
Bristol have already suffered a surprise defeat in the West Country this season, when they were beaten by the Pirates at Mennaye Field, while Jersey also showed that the top sides can be beaten by overturning Worcester Warriors at St Peter 10 days ago.
Although Sunday’s defeat in Cornwall was gutting for Albion, Dawe says the players have responded well in training.
“The players have got down to business,” said Dawe, who is now fully in charge of the team following Shanahan’s departure.
“It is just about preparing the team now for the game against Bristol.
“We just have to look to try and impose ourselves on Bristol.
“We got a slow start against the Pirates and we have got to avoid that against Bristol.
“Bristol are a team with a lot of star names and we show all teams respect, but we can’t be intimated by them.
“We have to make sure we have a clarity of mind of how we are going to play the game. We have to be crisp and concise and take any opportunities of field position Bristol give us.”
Albion are keen to just look forward now and try and pull off an unlikely escape.
If they do manage to beat Bristol or Moseley do not overcome Bedford then Plymouth would be in with a fighting chance to staying up as their next match would be against their relegation rivals.
A win at Billesley Common would guarantee the battle to avoid the drop would go to the final weekend when Albion entertain Doncaster and Moseley travel to Jersey.
Meanwhile, Albion have announced a sponsorship deal with GOD TV.
The company became involved with the club in January when they were facing administration.
Dean Seddon, head of development for GOD TV said: “We are so pleased to be supporting Albion. Plymouth Albion is a key part of the life of the city and we are pleased to be part of the club’s future”.
A spokesperson for Albion said: “Plymouth Albion welcomes the sponsorship from GOD TV.
“Albion has long had the reputation of being a great place to advertise and promote business.
“We have strong support from fans and from local businesses and we plan to build upon that in the future. With GOD on our side we are hopeful for the last few matches of the season!”
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