Carroll was making his full debut and told the Evening Chronicle: "Goals are very important for me for Newcastle and England.
"I came off the bench last month for England and I just wanted to get a start and show them what I can do - I think I achieved that. The game was all over the place - it was level at 2-2, then 3-3, but to get the two goals was brilliant for me.
"I thought I did OK, and to get the man-of-the-match award was brilliant. To score against Macedonia was important for me.
"I hadn't scored in the last couple of games for Newcastle, and it's a great feeling to score for your country.
"Scoring goals is important for any striker."