The young Swede bagged the first goal in Ajax's vital 2-1 success over the Italian outfit and Ibrahimovic was delighted with his performance.
"It went really, really well," beamed the striker. "That was nice.
"It's going well I feel and this is confirmation that I can manage in the Champions League."
Ibrahimovic admitted he had to be alert to poach Ajax's opening goal after Roma keeper Francesco Antonioli spilled Nigel de Jong's effort.
He added to Sportbladet: "It came from a rebound and I got the ball. First, I was thinking of shooting directly but it's a matter of being as clinical as possible.
"I kept the ball then shot. You have got to be awake."
Ibrahimovic also provided the assist for Jari Litmanen's decisive goal and the Swedish marksman believes the win in the Amsterdam ArenA demonstrates Ajax have strength in depth given the absences of Cristian Chivu and Rafael van der Vaart.
"It's good proof of what a good squad we have got," continued Ibrahimovic. "There are players who can come in and replace the others.
"We are not 11 men, we are 22 men."