Burke, who is still recovering from ankle surgery, could only watch as his team-mates lost 2-1 against FBK Kaunas on Tuesday to end their Champions League campaign at the first hurdle.
Without another UEFA Cup run to fall back on, the early departure from European competition has seen fans point the finger at certain players and manager Walter Smith's selection and signing policies.
"In any job if you are not doing the right thing, someone else will come in and take your place," the Scotland cap said. "It's as simple as that.
"As a football player you want exceed your own expectations and do as well as you can in each game, and better yourself each season.
"If you're not doing that, especially at a club like Rangers, it's under a magnifying glass and it's very difficult sometimes.