The Swiss striker was restricted to just 12 total appearances across all competitions for West Ham following an £8m move from Basel last summer.
"Yes, to be fair I deserved to play more, I don't need to hide that. I deserved that," Ajeti said.
"But this is football, this is how it is. I am really happy now. What is gone is gone and I'm looking forward now.
"I just think I need to play and this is why I signed for Celtic."