Bulls captain Pierre Spies said that losing to the Chiefs in their final match was frustrating having won two and lost two on tour.
The Bulls were leading 8-16 at half time but as the match wore on the Chiefs grew stronger and Spies admitted they let the result slip away.
"They put us under pressure at the breakdown and we couldn't get our game going, then they got that try," said Spies.
"We thought we had a chance but that try made it very difficult for us."
The Bulls finished their tour with a 35-41 bonus point victory over the Rebels in Melbourne, a 24-27 victory over the Waratahs but they also had a 16-11 loss to the Highlanders and today's 28-22 loss to the Chiefs.
The Chiefs lost their last match 42-27 to the Reds in Brisbane but with the help of a bye in between they recovered from the loss to take their record to played 12 and won 10 to date.
"We're thrilled that we could kick on in a very tight game," Chiefs captain Craig Clarke said.
"We didn't want to play a controlled, structured sort of game, that's more their style, we wanted to up the tempo a little bit."
The Bulls travel back to South Africa now as they host the Stormers next Saturday at Loftus Versfeld.