Woodward's men posted five tries during a blistering opening 21 minutes at Twickenham - but then went almost 50 minutes without scoring another point.
Italy dominated much of the game in terms of possession and celebrated a fine score in the corner from Mirco Bergamasco.
"I thought we showed a lot of heart and commitment. It's a young side," said Kirwan.
"But we cannot wait for 20 minutes until we start playing. We were getting too many people in at the contact point in the opening 20 minutes but we sorted that out and had more people ready for defence."
Kirwan expects England to go on and contest an RBS 6 Nations decider against Ireland in Dublin but he refused to predict the outcome for Clive Woodward's team.
He said: "I think Clive would be the opposite to me today. I think he would be very happy with the first 20 minutes but not the next 60.
"I thought they were quite outstanding during that time but you have to give Italy credit for coming back and putting them under pressure.
"I believe England can go on and set themselves up for a fantastic finale against Ireland."