EUROPEAN RUGBY: Les Kiss admits everyone is feeling the pressure after Ulster's latest defeat
The home team outscored their visitors by three tries to two at the Kingspan Stadium, but only briefly led the game and the loss - their fourth in six European games - meant the Irish province finished bottom of Pool Five in what was a dead rubber for both sides.
“It is not a nice place to be,” said Kiss, whose side had already lost any hope of making the quarter-finals before this error-strewn display.
The main concern for Ulster now is that they have lost their last four games and nine of their last 13, with their last victory coming just before Christmas against Connacht.
“I feel that weight (of pressure), for sure. But it is what my job is,” Kiss said. “It is tough to be in that space. It is.
“Some of us have been there once or twice, some a few more times, but there is a lot of good effort going in.
“We are not complete. We have made a lot of errors in the game but we are not that far away.
“But when you are in that space, you have got to look yourself in the mirror and you have got to take ownership and responsibility and make sure you stay strong about where you are going and what you are doing together.”
Captain Andrew Trimble, Franco van der Merwe and Darren Cave all scored tries for Ulster, the latter coming in the second half after the home side trailed 20-15 at half-time.
Paddy Jackson’s conversion of Cave’s 58th-minute try - the fly-half ended up kicking nine points - put Ulster in front for the first time in the game but Bordeaux, with Ian Madigan and then replacement Simon Hickey kicking 16 points between them, had the greater power and accuracy and also bagged first-half tries through Yoan Lesgourgues and Marco Tauleigne.
“It is important we recognise the responsibility and we have to get ourselves out of this situation,” added Kiss.
“That is what we are going to work hard on.”