The Westerners claimed a famous win over the 2006 finalists at the Sportsground on Friday, but if they are to have any hope of catching Harlequins at the top of Pool 3 they need to win again in France.
The English champions hammered Zebre in Italy on Saturday and are expected to do the same in London this weekend. They already have a six-point cushion on the Irish province, who they host after Christmas.
Biarritz are nine points off top spot and out of the running, meaning Connacht could take advantage if their eye is off the ball at the Parc des Sports Aguilera. The reigning Challenge Cup champions take on Stade Francais in a crucial domestic game a week later.
"I suppose mathematically there is a chance but it's going to be very tough," Balshaw acknowledged. "I presume we're going to have to get five points in every match from here on in.
"We're bitterly disappointed but all credit to Connacht. They deserved the victory and they were the better team.
"We're disappointed because we focused on the Heineken Cup; we want to make knockout stages.
"I hope we can regroup. We've got to improve dramatically. We are mid-season, we're mid-table (in the Top 14) and we want to be getting into the play-offs."
Many of Connacht's previous successes have been blamed by the losers on the levelling effect of bad weather at the Sportsground, but that excuse wasn't available to the French team last weekend.
"Everyone says going to Connacht, 'There's the wind, there's the rain,' but Connacht are a bloody good team and it was tough to play against them, especially with our error count," Balshaw said, before lamenting his side's inconsistency.
"If it was easy to fix, I'm sure we would have done it by now. There are a lot of individuals who have got to work on their own game. It's not just happened this season but last season as well.
"The individual error count is killing us, and especially when we are getting into scoring positions. That last pass, the last piece of play, is costing us.
"Connacht kept the ball very well. They were placed in parts of the field very well by Dan Parks and they made it very tough for us. They thoroughly deserved the win.
"As a collective they were very good. They threw the ball around very well, they kept possession, the pack were superb."