Sarries made it through to their fourth final in six years on Saturday thanks to a 29-24 victory over the champions at Franklin's Gardens.
"They are a very big, physical side and we knew we needed to match them," Burger told BT Sport. "The boys put in one hell of a shift today.
"It is no secret that they have had the better of us the last couple of times and we knew we needed to be at our best. We stood up physically. Every collision we were there."
Saracens will take on either Bath or Leicester Tigers in next weekend's final at Twickenham Stadium.