Sportal.co.nz 03.Mar.2013Getty Images
Despite having a significant amount of possession early in the match, they were only able to score one penalty to Johan Goosen.
Speaking to the media after the match, Drotske said that he was disappointed when he met with the team at half-time.
"I think after the first half, we definitely did most of the playing," said Drotske.
"I thought we should've got points on the board. In saying that I think the try just after half-time, where we kicked it against one of the Chiefs players was probably where the Chiefs got momentum.
"They played really well in the second half and we were outplayed in the second half."
Captain Adriaan Strauss said his side had responded well after an error-ridden performance against the Sharks a week earlier.
"I think we should have played closer to the forwards and we didn't," Strauss said bluntly.
"[The Chiefs] are a good defensive side and they were good on the night as well."
Drotske added that jetlag wasn't a reason for the heavy loss as history dictated it was the second game of a tour where players began to feel the effects.
The Cheetahs' second match of their tour is at Rugby Park in Invercargill, where they'll tackle the Highlanders on Saturday night.