The word 'though' has two functions. If it's at the beginning of the phrase it is equivalent to 'although', and if it's at the end it is equivalent to 'however/but'. The punctuation is also important.
1. You could say:
I know we didn't win, though I am happy with how we played.
Note that I've taken out the comma (,) 'Though' is part of the second half of your sentence.
2. I'm working on it but we have bigger problems at the moment, though.
I've added a comma here to separate 'though' from the rest of the sentence. In this sentence it means 'however', and is not an integral part of the sentence.