The Hammers were impressive on Saturday afternoon as they beat Liverpool 2-0 at Upton Park, with Carroll bagging the second goal against his former club.
That result took them up to sixth place in the table on 32 points, just one behind Manchester United in fifth and four behind Tottenham in fourth place.
West Ham are firmly in the hunt for a Champions League place at this stage in the season, but Carroll insists they are just taking things game by game rather than setting targets.
“The squad is great, the manager is great and the staff are great, and everyone’s enjoying it and that’s the most important thing,” he told whufc.com.
“Everyone is just looking at the next game. There is so much talk about the league table and that, but we just focus on the next game.”
“The manager keeps us grounded and looking at the next opponents and that’s what we’ve been doing.”
What will be a big boost to West Ham’s hopes of finishing high up the table this season is how they have managed without their star players over Christmas.
Slaven Bilic’s side were decimated by injuries, and while they went winless, the Croatian made them tough to beat and has negotiated a tricky period well without key players.
With those players now returning, notably Dimitri Payet, they will be confident that performances can get back to the level they enjoyed at the beginning of the campaign.