The ignore button can only be accessed through the scoreboard which is shown after the game.
It's not available in the scoreboard which gets displayed while the game is still in progress.

That means I can only ignore a player after the game is already over.
But I would like to be able to ignore a player during the match so he doesn't annoy me for the rest of the match.
It doesn't help me much that I can ignore him after the match is over because then he already annoyed me for the whole game. Of course it would help for the next match I encounter him but the odds of meeting him/her again are slim.

Screenshots of where the ignore button is missing: http://imgur.com/a/mauF8