Antonio's goal was his fifth of the season
David Moyes said he wants to take West Ham to the next level after they beat West Brom to move within two points of a Champions League place.
Goals from Jarrod Bowen and Michail Antonio secured a 2-1 win on Tuesday.
The victory moved West Ham on to 32 points after 19 games - their highest points tally at the halfway stage of a Premier League season.
"We're showing some growth in how we play and what we do," said Moyes.
"I'd like to dream a lot but we're very humble and understand we're West Ham, we're not going to start shouting things too soon because history has shown we haven't always backed it up and I want to be the one to back it up.
"We're going step by step and making good progress picking up points. I want us to be competing at the top end and to do that we have to keep winning."
West Ham took the lead on the stroke of half-time when Bowen chested in Vladimir Coufal's cross.
The visitors levelled soon after the restart through Matheus Pereira's thunderous drive from distance.
Dara O'Shea then blocked Manuel Lanzini's goalbound shot but Antonio gave West Ham the win with a hooked finish.
From then on, West Ham looked comfortable without threatening to add to their lead as they claimed a third Premier League win in a row.
Defeat for West Brom, meanwhile, leaves them 19th, five points from safety.
Antonio underlines importance to West Ham
Antonio has endured an injury-hit campaign and his start against Burnley at the weekend was his first since November.
But the striker made up for lost time by getting the decisive goal in that game and, despite concerns over how he would cope with starting a second game in three days, he was once again the match-winner against the Baggies.
Antonio is a deadly finisher inside the box, with all 41 of his Premier League goals having been scored inside the penalty area and he is integral to how Moyes wants his West Ham side to play.
They have become a defensively more solid side under the Scot - with West Brom's goal the first the Hammers have conceded in their past five games in all competitions - but they are also winning games by narrow margins, underlining the need for a player of Antonio's quality.
Moyes is looking to sign a striker in the January transfer window but keeping Antonio injury free for the remainder of the season will arguably be more important to West Ham's ambitions.
"We are looking to get him to get back to his level of fitness but he is certainly back to his level of goals because he is nearly a goal a game since he came back," Moyes added.
Another defeat, but some hope for Baggies
West Brom boss Sam Allardyce has forged a reputation for leading seemingly doomed teams away from relegation trouble but when he took over at the Baggies on 16 December, it looked like this would be a task too far.
They had won just one of their first 13 matches before Allardyce's arrival and lost three of his first four games in charge, conceding 13 goals and scoring just one in the process.
But a hugely impressive 3-2 victory at Wolves on Saturday has given Baggies fans hope that fortunes are starting to turn and although this game ended in defeat, there were signs of encouragement.
In a match of few chances for either side West Brom often looked a threat on the counter and could have snatched a point with more composure from Darnell Furlong, who flashed a volley wide in injury time.
Allardyce said: "Great response in the second half - we got our goal but you have to expect in the Premier League that the home team will put a bit of pressure on you and that pressure did come.
"So even though we did fight back and created a chance or two, ultimately we lost the game because their final-third play was better than ours."
-- Courtesy of BBC Sport