Bowen, who joined the Hammers from Hull City in the January transfer window, did not start against City and came on as a substitute in the 80th minute.
Moyes told BBC Sport: "I don't want loads of pressure on Jarrod Bowen to come in and help us. I am hoping in the coming months he can help us but I am trying to not put too much pressure on him."
According to WhoScored, Bowen scored 16 goals and provided seven assists in 29 Championship games for Hull this season before his move to West Ham in the January.
The 23-year-old forward made his Premier League debut for the Hammers against City on Wednesday evening.
According to WhoScored, the youngster had a pass accuracy of 75% and took seven touches.
The defeat to Pep Guardiola's side means that West Ham are third from bottom in the Premier League table at the moment with 24 points from 26 matches.
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