French hosts Clermont took the honours with a 22-16 victory at the Stade Marcel Michelin, stretching their winning run on home soil to a remarkable 75 matches in all competitions.
Tigers came back from 16-0 down to cut the gap to just three points before one final penalty from Clermont scrum-half Morgan Parra provided a little breathing space for the home side.
Fly-half Owen Williams capitalised on determined pressure from the Tigers with three second-half penalties – two from inside his own half – and the final attack of the game took the visitors almost within touching distance of the tryline.
Director of rugby Cockerill said: “Gallant loser is not really my thing, but we’ll take the positives from how we played.
“Clermont are a good side and they played very, very well. In the first half, they were as good as anybody has played against us and, with the atmosphere in the stadium, you can understand how they are so hard to beat here.
“We wanted to come here and win, and we gave it everything. We are a good side and should take credit for how we came back. There were two good teams out there.
“Fair play to the players. To come back and to be within one score of potentially winning it says a lot for them and their attitude.
“The defence on our line with 14 men was as good as any I’ve seen.
“It is the hardest place in world rugby to come and we were six points short, but we were still right in there at the end.
“It is obviously disappointing but there’s nothing but credit for the players for getting themselves back in there. The effort and the pride were outstanding.”
Tigers return to home territory on Saturday for an Aviva Premiership Round 19 fixture against London Wasps. Kick-off is at 3pm and tickets are available now. Phone the ticket office on 0844 856 1880 or call in at Welford Road. Or click here to book online.