Brett Pitman's fifth goal in as many matches took his tally to 15 since returning to the Cherries from Bristol City.
"Credit to my players. They have not given up and they showed that here," Laws said.
"If we put in similar effort over the rest of the season we have got a chance of succeeding. It is a pressure situation.
"We have a huge job on our hands and it is going to take a lot of effort to get out of this trouble.
"As I see it, I think it is between ourselves, Oldham and Colchester as to who goes down.
"We have to start scoring away goals. This was the fifth match in a row we have not scored away and it is a real Achilles heel.
"Mark Duffy's early miss in the second half epitomised what has been going on. He got into the goalmouth and did not even hit the target. He should have buried the chance.
"Bournemouth are the best footballing side in the division and it would not surprise me to see them go up automatically."