"If you break the game down, we were fantastic for 30 minutes, attacked very well and developed our game well, learning lessons from the way they defended," he said of the 24-15 defeat. "We kept the ball in hand, our breakdown was top class and they weren't competing all that hard.
"But we made silly mistakes and it gives them two tries, and all of a sudden you're going in and having to speak about lifting it and not being down when we should have been talking about putting our foot on their heads and finishing the game off.
"When these things happen – and they do happen – especially against such a great team, you are going to have points where the game isn't going your way and we've got to have the maturity to be able to stop that and make it hard for them.
"We were not a difficult team to play against for certain spells and, especially away from home, I'm a massive believer that we have to make it very, very difficult to get points against [us]."
Kellock made a similar speech this season, after his side lost successive RaboDirect Pro12 matches to Ulster and the Scarlets and they responded with four of the sort of hard-earned wins that was their hallmark as they reached the play-offs of that competition last season.
Clearly, it will be tougher to do that when their next opponents, Ulster, last year's Heineken Cup finalists, have had two extra days' recovery time following their defeat of Castres on Friday.
However, Kellock said Glasgow could not afford to concern themselves with any unfairness in scheduling and must instead draw confidence from what they did well yesterday.
"We've got the belief and it's been spoken about already," he said. "We've got a tough pool, but then we get the win next week and we're right back in it, pushing into the next couple of games. You put so much into a game, but what you need to do is bounce back quickly, and we gave that everything.
"Physically and mentally, we put our heart and soul into that game and we fixed a couple of mistakes, so if we do exactly the same on Friday as far as the commitment's concerned and just tweak a couple of things we'll get the win.
"That's one game in our Heineken Cup campaign and it's about moving forward. We learn from that and we make sure we get the win on Friday."
Glasgow's cause did not appear to be helped by having only two backs among their eight replacements for a game in which full-back Stuart Hogg limped off early, playmaker Ruaridh Jackson had to be replaced at half-time and the vastly experienced and influential Sean Lamont also went off injured.
However, Gregor Townsend, Glasgow's head coach, dismissed that as having been a factor. "When you go into a game you can't predict whether there are going to be injuries or not. We actually defended pretty well, or better when Chris Fusaro went into the centre," he said.