The Aviva Premiership outfit remain rooted to the bottom of Pool Four despite gaining a losing bonus point courtesy of Nick Evans’ drop goal with the final kick of the match in central France where Clermont had won their previous 64 matches.
Wing Tom Williams scored a 39th minute try and one point was what Quins fully deserved for a committed and spirited display at the Parc des Sports Marcel Michelin.
Quins captain Robshaw said: “We are disappointed not to have come away with more. You look at the record that they have here and credit to them.
“We gave them three early tries but stayed in it and leave with a point because of a cracking drop goal by Nick to finish.
The much-improved performance came just eight days following the below-par display at home against the Scarlets.
And Robshaw was delighted with the response of his team-mates after director of rugby Conor O’Shea revealed his anger at the players.
Robshaw added: “We had a telling off in the week, but we trained hard and well and came here with a point to prove.
Quins trailed 20-13 at the interval after Williams scored in the left corner following good work by Robshaw, Will Collier, Danny Care and Mike Brown.
But, despite a fifth loss in seven games this season, England flanker Robshaw claims the spirit is still high in the Londoners’ camp.
Robshaw said: “We thought we were very much in the game at half-time. We spoke about the quality in their side and if they scored three, we had to score four. That was our mentality all week.”
Clermont Auvergne scorers: Tries: Byrne, Fofana, Lacrampe. Cons: James. Pens: James 2.
CLERMONT AUVERGNE: Byrne, Rougerie, King, Fofana, Sivivatu, James, Lacrampe, Debaty, Kayser, Kotze, Pierre, Hines, Bonnaire, Lapandry, Chouly.
Replacements: Nalaga for Byrne (67), Delany for James (55), Radosavljevic for Lacrampe (48), Chaume for Debaty (53), Paulo for Kayser (53), Ric for Kotze (63), Jacquet for Pierre (66), Vosloo for Lapandry (50).
Harlequins scorers: Tries: Williams. Cons: Evans. Pens: Botica, Evans.
HARLEQUINS: Brown, Sackey, Hopper, Botica, Williams, Evans, Care, Marler, Buchanan, Collier, Easter, Robson, Wallace, Robshaw, Guest.
Replacements: Walker for Sackey (55), Smith for Botica (55), Lambert for Marler (77), Ward for Buchanan (18), Sinckler for Collier (45), Trayfoot for Guest (53).
Referee: George Clancy.