I tried running a dnd-next playtest and there was a particular problem that the party could not deal with monsters running away. This problem did not exist in 4e because of OAs.
Was there a rule that I have missed?
If not, how can I deal with it effectively? Players had different opinions on it. Some think that it is reasonable that monsters that run as fast as PCs can not be caught. Others think it is not.
You don't need a more general opportunity attack mechanic to just say "if you run off at full speed they get a hit in on you." This is how fleeing from combat worked in all D&D previous to the introduction of formalized battlemats in 3rd edition. All it gets you is one hit, though, so it's not really sovereign against fleeing. But consider adding a rule to this effect (I think it's clear that in 5e they are trying to return to you the GM being in charge of the rules instead of the rules being in charge of you, so don't hesitate to add things in you deem useful).
Or better yet, AD&D 1e, which only has 2 pages of combat rules in total, and somehow we still all used and enjoyed it...
a) You can add it and b) It doesn't have to be complicated.
Bonus: A slightly different take from Basic D&D's Rules Cyclopedia:
I kinda like that take on it because it takes a round to get up to top speed so there's one round of concentrated "Get him!"