The on-loan Liverpool striker scored the winning goal against Swansea on Saturday to end the Hammers' four-match winless run in the Premier League and lift them to 11th place
Carroll's clincher on Saturday was only his second of an injury-disrupted season but helped the Hammers move up to 11th in the Premier League.
Jarvis believes that West Ham have been unlucky not to collect more points in January but expects their luck to turn if they maintain their current level of performance.
"We've been playing well at home and creating all the chances, but maybe not getting the results we wanted or deserved," he told the club's official website.
"Getting the 1-0 win on Saturday is a massive boost to us. It takes us to 30 points and we can push on from there.
"We just have to keep doing exactly what we have been, creating the chances and hope that one goes in. This time Andy got a great header and it proved to be the 1-0 win we needed.
"It's a good three points to move on to next week, which will be a tough game away at Villa. But we're looking to go there full of confidence and get another result."
The former Wolves star reserved praise for Carroll's competitive edge in his first start since November.
"He's a great player, he wants to go and contest every ball, every cross, every goal-kick, every corner, everything! It's great to have him back in the team," Jarvis added.