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How can I get better at seeing checkmates

I played this game earlier today http://en.lichess.org/uZj2j3zy

It ended up as stalemate, but I should've lost even though I could have had mate in 1 earlier in the game but didnt see it.

How can I get better at seeing checkmates like this so I can win more games
The best advice is tactics. Try to do a few tactical puzzles a day until you see the complete solution (not just guessing). Set goals of doing 10-15-20 puzzles daily for a week each threshold. You'll see improvement gradually.
I suggest playing Classic games at start and thinking after each move, in your case, there is always a better move than you think of in the first place so try to play 10 minutes games and of course always think of a checkmate. Whenever you see opponent's king trapped or in uncomfortable position, analyse, think of what will happen if you move knight, if you move queen etc. And yes easy tactics to solve would be nice too.
Think of most positions on the checkboard as CAPTCHA checkboards.
Participate in 10-15 forum threads a day, and you should see improvement soon.
do not play bullet games first time.
order your thinking process:
in every position always look at all possible checks first
then at captures, then at threads. (for both sides)
play some correspondence games to get some experience in that new thinking order

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