'It's mission accomplished then, even though I feel I could have scored a couple more,' the Frenchman said on his website.
Anelka was loaned by Paris St Germain to Liverpool last season but manager Gerard Houllier decided not to offer sign him last summer.
'For sure I wanted to perform well in front of the Anfield crowd and Gerard Houllier, but there was no feeling of revenge.
'On my goals, I had the same spontaneous attitude, I kept my cool and I scored without making a fuss.
'I was simply glad to score for it had been a long time, two months roughly, since I last found the net,' he added.
'I was convinced it would come back and I'm glad it happened against Liverpool.'
Anelka was reasonably positive about Manchester City's season, with Kevin Keegan's side currently eighth in the Premiership.
He said it was 'not bad for a promoted side' and that their 'overall performance was positive'.
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