Edinburgh were the team on everybody's lips in round one after turning over Munster at Thomond Park but let that momentum slip following successive defeats to Connacht and Ospreys.
It was the loss to the Welsh region that hurt the most - shipping nine tries at the Liberty Stadium - which made their response against Scarlets all the more impressive.
Down by seven points, Burleigh himself crossed late on for a converted try to snatch a draw - and the utility back says Edinburgh are proving they are by no means a soft touch.
"We were more physical against the Scarlets, something we had been working on very hard," Burleigh told The Herald.
"There was an improvement, but we still made too many mistakes. The defence was better and hopefully we have shown that we can start winning games.
"We need to improve on the finer things and keep our composure at the right times. We put ourselves in the right situation in the second half against Scarlets and it was unfortunate we couldn't get over the line in the end, but it will stand us in good stead for Belfast.
"The guys have worked hard to get the spirits up and we aim to take another step forward."
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