With just five games to go, Raiders are 11th, nine points clear of third-from-bottom Dorking and the relegation zone.
A 10-8 home defeat to Chinnor last time out left Dawson’s side still not guaranteed safety but the Worthing head coach believes his side have enough quality to secure their place in the division.
He said: “We’ve been creating the chances in recent weeks but just not taking them.
“I’m sure we will in our upcoming games.”
Raiders return to action on Saturday with a tricky trip to second-placed Old Albanian.
After that, Worthing still have to face Canterbury, Clifton and Dorking at home, as well as a trip to Taunton Titans.
Dawson sees the home games as crucial and said: “We’ve got three winnable home games still to come.
“If we win those then we should be safe and I’m confident. If we play as we have, we will win them.”
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