The Irish province headed to south west France hungry to repeat their 22-14 victory from the previous round in Galway.
However, heavy rain showers and an unforgiving pitch played into the hands of an experienced and powerful Biarritz pack and kickers of the calibre of Dimitri Yachvili and Damien Traille.
The French side duly turned the tables on Connacht, running out 17-0 winners on Friday night with man-of-the-match Yachvili converting tries from Iain Balshaw and replacement Seremaia Burotu.
Speaking about the playing conditions at the Parc des Sports Aguilera, Elwood said: "We had prepared all week and we knew the weather was going to be poor, but we didn't know it would deteriorate like that.
"We knew it was going to be a huge challenge and the conditions did not suit us, but we were in a good space. However, unfortunately if you make mistakes at this level, you get punished."
Elwood acknowledged that it was difficult to establish field position and that Connacht's kicking game let them down, with Dan Parks struggling to exert much influence.
"When you are playing in conditions like that, it's nearly a disadvantage to have the ball. Our kicking game was not at its best today and we got severely punished.
"We couldn't get the yardage in our kicks and we struggled in that area today. It was disappointing that in the kicking battle we lost out today."
Balshaw's try on the half-hour, coming from a Traille half-break, was the most important score of the game according to the Connacht boss.
"It was always going to be a tight game in those conditions, but at 3-0 we were very much in the game. However that defensive error cost us and derailed us," he admitted.
"I think if we had gone in 3-0 at half-time it could have been different, because we would have had the momentum in the second half with the wind behind us. But that score gave them the buffer they were looking for."
Despite the round four loss, Elwood said there was still satisfaction in his young side having beaten the Basque outfit in Galway, if not in Biarritz.
"We take a lot of satisfaction from last weekend's win. We were looking forward to playing on a nice dry track, it would have been nice, but they are a big team and we are not the biggest.
"It's not our style of play to play into that, and when you have to go toe to toe with the heavyweights, it can be difficult on nights like tonight."
Elwood also dismissed suggestions that the controversy over Mike McCarthy's move to Leinster, which was announced earlier this week, had affected the squad's preparations for the Biarritz rematch.
"Mike told the coaches, he told the CEO and we told all the players, and we went on with our business.
"These things happen in rugby and we get on with our business in a professional matter - it's not an issue."
Balshaw said his team had concentrated all week on cutting down the error count in an effort to redeem themselves after last weekend's shock defeat to Connacht.
"We improved dramatically from last week. It was going to be difficult for both teams in the conditions, but last week we made 32 turnovers and in this competition when you make that many turnovers, it will cost you," he said.
"This week we focused on cutting individual errors out and concentrating on our basics, and we did that tonight. We put a lot of pressure on Connacht, cut down on errors and we came away with the win.
"We handled (the weather) a little better tonight, just like last week Connacht handled the game a lot better than us."
Balshaw said second-placed Biarritz are still in the hunt to qualify for the Heineken Cup quarter-finals but with Harlequins in control of the pool, next month's concluding matches will decide their fate.
"We've still got a possible chance of second place, but we just have to make sure in the next two games (against Zebre away and Harlequins at home) which will be very tough," he said.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.