Yes, when you use a single (positive) supply, the op amp needs to operate in the positive region. This means the waveform has to occupy the region between 0V and supply V.
Therefore your AC waveform needs to have a DC component added at the input.
You would have an easier time if you were to start off powering the op amp from a bipolar supply. That would provide both positive and negative regions for the waveform to operate in.
It would help if you were to make everything operate properly with a bipolar supply, then decrease the negative supply bit by bit, while you adjust component values to maintain the correct waveform in the positive region.