Speaking on the eve of the second Test in Galle, Mathews said last week's dramatic win in the series opener in Pallekele had banished the gloom in the home dressing-room after a string of defeats.
And Mathews said his team had a game plan for each of the tourists' leading batsmen who have struggled to adapt to the extra turn on Sri Lanka's pitches.
"The feeling is great in the camp after the beating we had got in the last six months," Mathews told reporters.
Sri Lanka have endured a torrid 2016, losing their crown as T20 champions after being knocked out in the group stages, before a tour of England where they failed to win any of their nine internationals.
But they showed they remain a formidable side at home by beating Steve Smith's world number one side in Pallekele, thanks to a maiden century from Kusal Mendis and another five-wicket haul by their lead spinner Rangana Herath.
"We have got to be cautious and we can't write them off. They didn't get runs, but they are a dangerous top order," Mathews said.
"We can't let them off the hook and we need to be on our money from the start. It's tough to play spin here."
Smith was the only Australian to pass 50 in the match and they all struggled against Herath and fellow spinner Lakshan Sandakan.
"We have got to be cautious about their batsmen who haven't got runs. We have got to stick to the plans and good bowling will win us the game.
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