Allardyce hails Carroll's match-winning performance
Allardyce declared it was 'a bit scary' to imagine how good West Ham might have been this season if Carroll had been fit for the entire campaign.
The 25-year-old forward missed the opening 20 games of West Ham's Premier League season but showed how crucial he is to Allardyce's team at the Stadium of Light, scoring one goal and creating another, as the London club registered their sixth win in nine matches.
"It's a bit scary to think where we might be if we'd had Andy all season," Allardyce said in his post-match press conference.
"We didn't have him all season last season and finished 10th. We've had him even less this season and we're now into 11th. We're one point behind last season's total (at this point)."
Allardyce said Carroll has all the tools to dominate the Premier League if he can stay fit for an entire season.
"It's an all-round quality that he has; quicker than he looks, some good hold up play off the chest at times, takes the ball with his feet, got a terrific shot on him … superb in the air and he's young," the 59-year-old said.
"So, hopefully, he keeps on … growing in terms of his experience and his abilities to stay fit and be an even better player than he already is."
Carroll scored West Ham's opener against Sunderland with a trademark header at the back post in the ninth minute and then chested down a long pass five minutes after half-time for Mohamed Diame to score the visitors' second goal.
While Adam Johnson pulled a goal back for the hosts in the 65th minute, Allardyce was generally pleased with his team's entire performance.
"Andy, using his major strength to put us 1-0 up. Beautiful header and I think that gave everybody the confidence to try and go on, and play, and expose more of the spaces that Sunderland were going to leave," Allardyce said.
"Because they were going to have to come out even more to try and get back in the game … and we finally took advantage of that just after half-time.
"Then really, we controlled the game even more from there on, didn't get the third when Stewart Downing went through and then had a little bit of a mad 20 minutes to hold on when (Adam) Johnson scored a very good goal.
"The lads, defensively, did that very, very well indeed and it's an outstanding victory for us."
Allardyce added that West Ham have just about avoided relegation with their strong run since the start of February.
"We're probably in the top four or five in the Premier League for results at the moment and it's got us out of trouble and it's got us almost safe; not quite mathematically but I think it'll be difficult for anyone to catch us now," he said.