Robs drink, depressed by criticism (6,2)

I believe the answer is:

sticks up

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'robs' is the definition.
(sticking up is a kind of robbing)

'drink depressed by criticism' is the wordplay.
I cannot really see how this works, but
'drink' could be 'sup' (to sup is to drink) and 'sup' is found in the answer.
'criticism' could be 'stick' (giving someone stick is criticising them) and 'stick' is present in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Telegraph.

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