Exeter kept their own slim prospects of progressing to the European Champions Cup quarter-finals alive with this hard-fought 31-19 victory.
The bonus point win saw the Chiefs leapfrog both Ulster and Bordeaux into second place in Pool 5.
Ulster’s defeat without a bonus point effectively ended their hopes of advancing.
“We didn’t look after our ball and gave away easy penalties,” Kiss said. “There were a lot of good things from us but they worked us over in the early period of the second half.”
Thomas Waldrom and Michele Campagnaro both scored two tries for Exeter. There was also a penalty try award, with Gareth Steenson adding three conversions.
The explosive Charles Piutau scored two tries for Ulster and Sean Reidy the other, with Paddy Jackson converting two. The feature of the game was a brilliant duel between wings Jack Nowell and Piutau, which thrilled the Sandy Park crowd.
Ulster stunned their opponents by taking a second-minute lead with a superb try. From a line-out 45 metres out, Stuart McCloskey sailed past Ian Whitten’s tackle to race away and create a try for the supporting Reidy.
Jackson missed the straightforward conversion.
After the first quarter Chiefs drew level with an excellent try which began deep in their own half. The hosts secured a turnover before some good ball retention and well-timed passing gave Campagnaro the chance to sell a dummy and run the remaining 20 metres to score.
The home side were becoming increasingly dominant as the game progressed and were rewarded when Waldrom forced his way over from close range.
Ulster suffered a further setback when prop Ross Kane limped off to be replaced by Jonathan Simpson but immediately overcame the blow by scoring a second try.
It was a brilliant solo effort from Piutau, who side-stepped three defenders for the try which Jackson converted to make it 12-12 at the interval.
Exeter began the second half strongly and their third try came after 50 minutes when Waldrom forced his way over for his second before another skilful move saw Exeter get their bonus point just three minutes later.
An exquisite pass from Phil Dollman sent Nowell away before the wing released Campagnaro to score his second try and Exeter led 24-12 at the end of the third quarter.
Ulster came right back into contention with their third try when Piutau collected a clever cross-field kick from Jackson to score and set up a tense finish.
The visitors were narrowly denied a fourth try when David Shanahan narrowly failed to win the touchdown after another superb run and kick ahead from Piutau.
Steenson missed a penalty as Exeter’s nerves jangled but Chiefs secured victory after 70 minutes when referee Roman Poite awarded a penalty try after Jackson knocked down a scoring pass from Nowell, with the outside-half also yellow-carded.
“I’ve no complaints about the yellow card as they caught us out and put us under pressure and we didn’t handle it,” said Kiss.
Tries: Campagnaro 2, Waldrom 2, Penalty. Cons: Steenson 3.
Tries: Reidy, Piutau 2. Cons: P. Jackson 2.
Dollman, Nowell, Campagnaro, Whitten, Woodburn, Steenson, Lewis, Moon, Cowan-Dickie, G. Holmes, Lees, J. Hill, Johnson, Armand, Waldrom.
Devoto for Whitten (63), Townsend for Lewis (67), Low for Moon (59), Yeandle for Cowan-Dickie (59), Williams for G. Holmes (59), Dennis for J. Hill (63), Horstmann for Johnson (54).
Ludik, Piutau, L. Marshall, McCloskey, Trimble, P. Jackson, Shanahan, Black, R. Best, Kane, Treadwell, Browne, Henderson, Henry, Reidy.
Stockdale for L. Marshall (60), Herron for Trimble (72), Warwick for Black (45), Andrew for R. Best (77), Simpson for Kane (33), van der Merwe for Treadwell (63), C. Ross for Browne (54). Not Used: P. Marshall.
Romain Poite (France).