Loan star Carroll got off the mark for West Ham with a consolation goal in the 3-1 defeat by Tottenham on Sunday.
Allardyce was happy to see Carroll break his duck and he is confident the 23-year-old will thrive at Upton Park if they play to the striker's strengths.
"It was brilliant for him and about time too, to be honest," said Allardyce.
"It hasn't meant anything to us but it gets him off the mark.
"It shows the rest of my players if we put the ball in the right area, Andy will score."