Carroll's time at Upton Park has been blighted by inconsistent form and a knee injury that kept him out of the Hammers starting line-up for two months.
But Carroll did not struggle one bit on his return to the first-team, bullying the Swansea back-line before heading home the winner with 13 minutes left.
The 24-year-old, who is on loan from Liverpool until the end of the season, was left out of England's squad to face Brazil next week but his manager thinks the striker will be under consideration for the Three Lions' double-header against San Marino and Montenegro in March if his form continues to improve.
"He should (get back in)," Allardyce said. "As long as he can stay fit between now and the end of the season, get as many games as he can (he will).
"There is a lot more to come from Andy. If he produces better performances than he has here, and if he builds his goal tally up, finishes the season on a high, it will be great for us and it will be great for him. At the start of the season it was disappointing for him because of the injuries but hopefully he can finish the season on a high."
Allardyce was impressed with how Carroll came through the match given that his only other appearance in the last two months was a brief cameo off the bench at Fulham in midweek.
"It was his first full 90 minutes in nine weeks," Allardyce said. "But when you looked at him it didn't look like any fatigue was there. He looked like he was enjoying himself and [Kevin] Nolan always seems to know where to go (when Carroll plays). He could have had a couple but their keeper [Gerhard Tremmel] had a stormer."
West Ham looked like being dragged in to the relegation zone after a run of one win in 11 matches but the victory means they are nine points clear of the bottom three.
"We were under big pressure to produce a result," Allardyce added. "I thought we thoroughly deserved the win. The way we've been playing at home has been fantastic all year. It brought us the victory but it was a shame it wasn't by more."