Will using irf4905 & tl431 need some change in the resistors value, especially Potentiometer value?

Should not.

 

This circuit idea is with separate on and off adjustments. You need to tweak the circuit to fit the purpose, but you get the idea.

 

The Circuit I provided works great just as drawn.
You may be having problems with the setup of your simulation.

Also, your Power Supply is 13.5-Volts,
and You say the Circuit won't work below 13.5-Volts.

Do You understand the concept of the FET turning "Off" any time the
Voltage at the "Reference" Pin drops below 2.75-Volts,
and the FET turning "On" ONLY when the "On" button is pushed ?

The Values of the Resistor and the Pot, combined together,
set the Voltage at the "Reference" Pin,
and determine the cut-off Voltage.

3- simple calculations have to be done to determine what the Voltage-Range
of this Circuit will be .........
1) Voltage at Reference-Pin when the Pot slider is moved all the way to Ground.
2) Voltage at Reference-Pin when the Pot slider is moved to the center position.
3) Voltage at Reference-Pin when the Pot slider is moved
all the way towards the Resistor.

The Resistor, and the Pot, effectively form a 3-Resistor "Voltage Divider".
.
.
.

 

This circuit idea is with separate on and off adjustments.

You need a stable 4V supply for your posted circuit.
Where is that coming from?

Also D2 will cause the circuit trigger point to be temperature sensitive.

All in all, a more complex and inferior circuit to the one LQC posted.

 

You need a stable 4V supply for your posted circuit.
Where is that coming from?

Also D2 will cause the circuit trigger point to be temperature sensitive.

All in all, a more complex and inferior circuit to the one LQC posted.

As I said: " You need to tweak the circuit to fit the purpose, but you get the idea."
Who ever uses the circuit should know what one is doing and be able to modify it accordingly.
4V is a reference, build a reference supply. D2 is not necessary in this application as this is the battery input.
This is originally a solar shunt regulator but is easily modified to battery cut off circuits.

There are plenty of ways how to build things, just choose what you like and build your own creations.

 

Who ever uses the circuit should know what one is doing and be able to modify it accordingly.

I suspect the TS may not be that person.
(But apologies if he is).