The England striker's aerial prowess was on show as he nodded down for Kevin Nolan to score twice, with the three points moving West Ham out of the Premier League relegation zone.
Carroll was making his first league start at Upton Park of the season after being plagued by a foot injury, although his game ended on a sour note as he was sent off for clashing with Swansea defender Chico Flores.
Nevertheless, Allardyce was happy with what he saw from Carroll and Nolan, and expects the striker to be hitting the net before long.
He said: "We got quality finishing, which is something we've been striving for on a consistent basis and we've crawled our way out of the bottom three. We keep doing it the hard way.
"Andy's not at his best either, but once the players start feeding Andy with the right service, his ability to hold the ball up and cause problems aerially is obviously his main threat.
"He just needs to start scoring a goal or two which is now his next challenge.
"He's made two for Kevin, next game let's make another couple and score one yourself.
"Nolan's contribution all over the pitch was a proper captain's contribution and you can see that by what it means to him to score goals."
