What meaning of 'suppose' do you believe would fit here?
'You cannot suppose I had a late night just because I yawned' is possible, because the person is assuming something with very little evidence.
"I suppose he could be too tired to drive anymore. I've seen him yawning a lot" - again, something is being assumed from just a little evidence.
The meaning of your sentence seems to be, 'you can't imagine just how exhausted I was' - 'you can't imagine' is a stock phrase:
"You can't imagine just how embarrassed I was."