When you "criticise" you are naming an error , a mistake , a mindless inaction briefly or in details .
When you "blame" on the other hand there is an emphasis on discrediting the other assigning him/her responsible for the mistake or deficiency or whatever is being criticized from your side !
Don't criticize him !
Means don't mention his errors mistakes , flaws or any negative attitude !
Don't blame him !
Don't hold him responsible for these flaws and mistakes !