Bad Beat or Bad Play?

[Fredrik]

I'm somewhat new to the game; and enjoy playing both free multiboard tournaments (more for learning how to read players and recognize good/bad flops than actual playing experience) and one table tournaments for money (Just moved to 10/1 instead of 5/1, as I had to have much higher winning rate on 5/1 to 'get even')

Yesterday; I played a 10/1 table and got this play:
Party Poker No-Limit Hold'em Tourney, Big Blind is t15 (8 handed) converter

CO (t775)
Hero (t770)
SB (t695)
BB (t800)
UTG (t1055)
UTG+1 (t1190)
MP1 (t760)
MP2 (t1955)

Preflop: Hero is Button with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/club.gif[/img].
UTG calls t15, UTG+1 calls t15, <font color="#666666">3 folds</font>, <font color="#CC3333">Hero raises to t30</font>, <font color="#666666">2 folds</font>, UTG calls t15, UTG+1 calls t15.

Flop: (t115) 6[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
UTG checks, UTG+1 checks, <font color="#CC3333">Hero bets t65</font>, UTG calls t65, UTG+1 folds.

Turn: (t245) 9[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
UTG checks, <font color="#CC3333">Hero bets t100</font>, UTG calls t100.

River: (t445) A[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
UTG checks, Hero checks.

Final Pot: t445

Results in white below: <font color="#FFFFFF">
UTG has 8c Ah (one pair, aces).
Hero has Kh Kc (one pair, kings).
Outcome: UTG wins t445. </font>

I'm not sure how I could have played it better. Can anyone give me some pointers?