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A new survey by customer satisfaction research firm ForeSee has found that luxury shoppers are not getting the kind of service they expect from retailers catering to the high-end market.

The top scoring retailers in ForeSee’s Luxury E-Retail Satisfaction index were Coach Inc. (NYSE: COH) and Tiffany & Co. (NYSE: TIF) tied with a score of 80 on a 100-point scale. That score barely indicates excellent service. Saks Inc. (NYSE: SKS) and Nordstrom Inc. (NYSE: JWN) tied with 79 for second place.

The lowest scoring e-retailers were privately held Rue La La and Gilt, with scores of 73 and 72 respectively. For the entire luxury sector the aggregate index score was 77.

Luxury retailers do not score as high as many other online retailers. The top scorer among all e-retailers in ForeSee’s December survey was Amazon.com Inc. (NASDAQ: AMZN), with a score of 88. And there were at least a dozen other e-retailers with scores above 80, including Kohl’s Corp. (NYSE: KSS), Apple Inc. (NASDAQ: AAPL) and Walgreen Co. (NYSE: WAG).

The good news for luxury retailers is that their shoppers are more likely to use mobile devices to do their shopping, indicating a comfort level with both the security and ease of mobile e-commerce. An executive at ForeSee draws the conclusion:

Mobile is a huge area of opportunity of any retailer, but particularly for a luxury brand. Our study shows that luxury brand shoppers are already adopting the mobile channel faster than non-luxury brand shoppers. It’s now up to those retailers to deliver what luxury customers want from mobile in order to keep them coming back to the brand and to influence purchases across all channels.

And what do customers want? According to ForeSee’s survey, 41% complained that prices were too high. However improving merchandise selection and improving the e-retail site would have a bigger impact on both customer satisfaction and return on investment.