Should I admit I let my daughter win when she asks directly?

My six-year-old studied the board and said, "You could have taken my last piece. Did you lose on purpose?"

I had. She'd lost twice, knocked the counters off the table and said she was never playing again. I wanted our Saturday afternoon back, so in the next round I made a move I knew was wrong. Her older cousin spotted it and gave me a look.

Now my daughter is asking whether the win counts. I said I was distracted, which was another decision made for my convenience. She has been telling her dad she beat me, and I haven't corrected it.

I don't want every game to turn into a lecture about disappointment. I also don't want her checking my face for clues that the result was arranged. Would you admit the deliberate mistake and start again, leave this particular win alone, or change how we choose games while she is finding losing difficult?