The 47-year-old received a huge welcome from the Selhurst Park crowd before his first home game in charge, with Palace making a positive start.
Eddie Nketiah and Daichi Kamada both went close before Erling Haaland opened the scoring for City.
Sage acknowledged the difference in quality while insisting his team must continue working and improving.
"I'm frustrated. I think the scoreline is heavy, because we were in this game for 65 minutes.
"We created some chances from the beginning until they scored the third goal. Then the psychology of the game changed.
"We know we were a bit late in our pre-season. It's why we were good for 45 minutes in the last game and 65 minutes today.
"The bad moment is at the 3-1. We came back. We lost our hope in this situation.
“I think you saw how we want to play for 60 minutes, last time it was 45 minutes. The next game I think we can play the entire game the way we want.
"Before of that, we had a lot of chances which we missed. Against a team like this you need to be at your top (level).”