Claudio Bravo was sent off for City, but the hosts couldn't take advantage.
“At the end, we had the conditions to win the game, with them down to 10 men and an outfield player in goal," Gasperini told Sky Sport Italia.
“Unfortunately, there was very little football in stoppages and that showed our lack of experience. They took so long over the substitution and then tried to keep it at the corner flag.
“Sometimes it happens to us, we need a wake up call and in this case it was the missed penalty, as from there we really did change gear.
“We still have a chance in the Champions League, but I would be very happy with a place in the Europa League too, as long as we continue some European experiences and can grow.
“Our performance with Shakhtar wasn't bad at all and we could've won that. We could've won tonight too, whereas in Manchester we played in fits and starts. If we can play with consistency, then we can win games at this level.
“We struggled in the first half, as City scored early and every time they came forward, they caused problems. The trouble is that sometimes you think you're at your best, but you're not. If you are just a metre behind, these opponents can keep the ball constantly and pin you back.
“Manchester City are excellent at going forward, but they struggle at the back. So we had to take some risks, we raised the level of what we thought was the maximum, started to move it quicker, get the ball back, win tackles and in that second half we created more scoring opportunities and played better than Manchester City. We're not dead yet!"