Hi. As Keiko-san said, it is hard to find a Japanese word for "deserved to win". I believe you want to cheer him up because you know how hard he practised for the match. So I will suggest what I would write in this situation based on your English sentence.
「でも、Aさん(A=your friend's name)は試合のためにすごくがんばって練習したよ。勝ちにふさわしいぐらいがんばったんだから、元気出してね。次の試合で勝てるといいね。」
You didn't write the "元気出してね。次の試合で勝てるといいね。" , which means "Cheer up! Hope you will win the next game.", but I would probably add that kind of thing to cheer my friend up.
By the way, I like Nelson Mandela's word, "If you talk to a man in a language he understands, that goes to his head. If you talk to him in his language, that goes to his heart."
Please cheer him up with your Japanese and it will go to his heart :)