Liverpool laboured to a hard-fought victory at Turf Moor courtesy of a second-half winner from Raheem Sterling.
And Rodgers believes Can, who came on for the second 45, showed real ability after being introduced against the Clarets.
"The players deserve huge credit, because even though we hadn't played so well in the first half, we actually defended reasonably well," Rodgers told reporters after the 1-0 win.
"We got our blocks in, stopped crosses and with anything that did come into the box, we got up to the ball and defended really well.
"We needed to show a bit more composure on the ball in the second half, so we made a change with Emre [Can] coming on [at half-time].
"He showed really good athleticism, power and football ability in that position. What we had to do and defend, we defended well. It was a great three points and I'm delighted with them."