Reporting Players From Match History
Currently you can only report players immediately following a game in the post game screen, which is a little unfortunate, but it means that the context of that last match is most likely fresh in your mind. However, after your game you aren't always fortunate to end up in the post game screen and therefore cannot report a player from that match. I think the usual cause is a hiccup on PVP.net, so you get the black waiting screen, allowing you to either wait for nothing to happen, or to skip to home.
Now, the client has come a ways in the last year or two so that we have more information available to us, specifically related to our match history. We can see the champions played in the game on both teams, and not just our own. So, if we added the ability to report players from there it would keep some of the context from that game, which I'm not sure but I think that's part of the reason why we can't already report players outside of the post game screen.