Cryptic crossword puzzles are not everyone's cup of tea, but once you get the hang of it, they are relatively easy to solve.
You need to learn how to read the clues. There is always a pattern, and there is one in the clue that you found in The Hindu.
Cryptic crossword puzzles have indicators, which you need to recognise, to be able to solve the clue. There are different types of clue indicators.
The clue here is - Not say no to say except.
The solution, as you mentioned is 'accept'. If you look at the clue, you'll notice that 'except' and 'accept' are homophones. The clue, in this case, has a homophone indicator. Clues with homophone indicators have a word that has a reference to either an auditory or vocal expression. Here, that word is 'say'.
The clue in the puzzle is in two parts – not say no – which is the direct clue, and the second part – to say except – which is the homophone indicator (clue). You need to work the two parts together to get your answer.
Cryptic clues often make no sense, but they have a pattern of rules. Hope this clarifies your confusion and everyone else's as well.
'A love affair with knowledge will never end in heartbreak' - Micheal Garrett Marino