Bulls captain Victor Matfield and coach Frans Ludeke were left cursing their luck after drawing 34-34 with the Chiefs at Loftus.
The champions looked set for their second away defeat on the bounce until a late tries from Matt Symons and Aaron Cruden levelled the scores.
Despite their number of off-season departures the Bulls sit third in the South African Conference, but know Saturday's game was a missed opportunity.
"Anything else than a victory at home feels like a loss. We'll take the two points, it is against the champions but we should have had five," said Matfield.
"With 25 minutes to go at altitude we should have done better."
Ludeke focused on a decision to kick for goal rather into the corner late in the second half as one that may have cost his team the win.
"It was there for the taking, I thought we played well the 30 minutes after halftime where we were on top of the Chiefs, we scored some lovely tries and built an innings," said Bulls coach Frans Ludeke.
"But credit to them for the way they came back at us, to score those two tries, they worked hard for it.
"We actually gave them too much ball to play from, I think if we held on to the ball a bit more, we could have put them under pressure more we should have got that fourth try," he said of the final 10 minutes of the clash.
"With six minutes to go we went for poles, which if you think about it maybe if we went for the corner and kept them in their half and score a try it would have been game over.
"In that last 15 minutes we weren't accurate enough, on attack we didn't build more than three phases and lost the ball and we made silly mistakes on defence."