Following a difficult start to the campaign for last season's Premier League runners-up, Liverpool have taken 11 points from their last six games.
Sterling scored the winning goal in Friday's hard-fought 1-0 victory over Burnley at Turf Moor and the England international feels Liverpool are well set to move up the table.
"We're just taking it step by step. In the last few games, you can really see the belief back in the boys," he told the club's official website.
"Even at difficult times, you could see we are sticking together and trying to grind results out.
"It's massive for us to stick together and try to play the football that we know we can play. Hopefully that can get us the wins over the next few games."
Liverpool can move level on points with Swansea City when the sides meet on Monday, before Brendan Rodgers' side take on struggling trio Leicester City, Sunderland Aston Villa early in the new year.
Sterling knows a positive festive period could have a big say in what Liverpool can achieve this season, with a top-four finish still on his agenda.
"We didn't start off as well as we would have liked this season," he added.
"But if we can stick together over the next few weeks - it's a difficult time with games coming thick and fast - and come out of the Christmas period with a decent few wins, we can be right in there towards the end of the season for a top-four push."
