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 !

To criticize or criticise can be to look at what someone has done and to identify the poor work, suggesting improvements. However it can also just mean to identify the poor work. To blame is to point who or what caused the problem. So in an accident you could say that 1) the car was not well maintained 2) the road was poor 3) there was fog about so you could criticise the each issue but you might heap the blame on the driver who knowingly drove a poor car on a poor road in the fog. Basically you seek retribution from the person to blame but you can suggest improvements to those you criticise.