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Victory may have only been secured with a minute-and-half remaining in Belfast but the Irish outfit were good value for the 9-6 win that gives them a great chance of reaching the knockout stages of Europe's premier club competition for the first time since 1999.
And Court, who has played 70 competitive games since joining Ulster for the 2006/07 season, insists he has never enjoyed a win quite so much.
"This is the biggest win Ulster have had ever since I've been here," said Court.
"It means everything to us. For us it was just a matter of staying tight and tough and keeping the discipline.
"But, unfortunately, the job is not done yet. We're neck and neck with Biarritz on points and there's still another week to go.
"Even though we needed to win against Biarritz, obviously we can't start celebrating and getting too ahead of ourselves."
Those sentiments were echoed by Ulster head coach Brian McLaughlin, who lauded his side's efforts but insisted there is still plenty of rugby to be played.
The former European Champions travel to Italy to face tournament newcomers Aironi next weekend knowing another victory would likely ensure qualification one way or another.
But with the pool still in Biarritz' hands courtesy of the losing bonus point they picked up yesterday, Ulster certainly aren't getting carried away.
"Our defence on our line halfway through the second half was unbelievable," added McLaughlin.
"We've talked long and hard about the trust we have in each other and the trust in our system.
"Our defence was outstanding and we forced the error. We took their purple patch and we matched it. We got the turnover and got the penalty we needed and Ian Humphreys put it over, which was fantastic.
"We know the pool is not entirely in our hands, but the fact is that we got the win against Biarritz in exceptionally tough conditions.
"We know we have to go to Aironi and we're under no illusions that we've got to go there and get the win - if we get a bonus point, even better.
"We can't do anything about Biarritz and we have to hope that Bath go there and do a good job. But we can't worry about that - we've got to take care of business ourselves."
