McCall's men lost 4-0 on aggregate but, already trailing 3-0 after the first leg, they acquitted themselves well in Russia on Thursday, losing just 1-0 to a team who are unbeaten in the Russian Premier League since November.
The only goal came when Stephen McManus headed into his own net five minutes after the break and Bob McHugh missed from the spot when he had a chance to level in the final minute.
McCall said: "I was proud of them, it was a good effort.
"I have watched them (Kuban) four times and I watched them on Sunday against Spartak (Moscow), and they are a really good side.
"They are talking about (Ibrahima) Balde going for £10-11m and the boy in the middle (Charles Kabore) for £7-8m.
McCall: They didn't cut us open
"The focus was the game tonight, to get to half-time and be in the game and then, if we could get ahead, to start thinking about the tie.
"Their opportunities came from two or three of our errors, they didn't really cut us open. I have seen them cut some really good teams open.
"Then they got the goal and we rocked for about five minutes, but we battled away and it would have been the icing on the cake if we had scored at the end.
"The effort and determination was good and we're just disappointed to lose the game.
"Bob's disappointed and Mick (McManus) is disappointed but they have no need, people miss penalties and score own goals. It's part of football."