The Scottish side are one of only two teams in the Challenge Cup who can boast a 100 per cent win record.
But Gilchrist's team have been unable to translate their form on the continent into success on a domestic front.
Edinburgh currently lie in eighth place in the GUINNESS PRO12 and are struggling under the weight of a lengthy injury list.
Gilchrist himself is fighting to regain fitness after fracturing his arm against Lyon back in October.
But while Scotland's captain must remain on the sidelines he is urging his teammates to focus on gaining some consistency in their league campaign.
"I think league position has a greater importance," Gilchrist told the Edinburgh Evening News.
"I was lucky enough to play in the European semi-final a few years back which was very special but I think we have a reputation for being inconsistent in the league and that's something we're working hard to address.
"We can beat anyone on our day but we need to find that consistency to really push up the league and target a top-six finish that will guarantee a Champions Cup spot."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland