The Cherry and Whites saw their qualification hopes dealt a major blow last weekend with a 32-9 defeat at Sale Sharks.
Despite that result leaving the club five points off the top four with two games left to play, Burns believes that they can enjoy a successful end to the campaign.
"We're still in with a shout of the top four but we do need other results to go our way now," the England international told Gloucester's official website.
"However, if we win our last two games, who knows? We've just got to keep plugging away and get our performance back on track."
Gloucester take on league leaders Saracens at Kingsholm Stadium on Saturday.