The last nine days has seen the gap between a number of teams close dramatically in the top half of the table, with Hearts now just nine points behind third-placed Hibernian.
Full-back Lee Wallace last week insisted Hibs could be caught.
Midfielder Stevenson was more cautious but reckons Hearts will have a better idea where their ambitions lie after their upcoming games at Aberdeen and Dundee United.
"I'm not really looking at Hibs or anything really above that," said Stevenson, who signed from Ayr on transfer deadline day.
"We're just looking at ourselves and doing well, trying to maintain where we are.
"I think the next two games will be a big test, away to Aberdeen and away to Dundee United.
"We'll see where we are when we make it through those two games."
The Hamilton win was Hearts' second in a row since Jefferies returned as manager last month.
Keeping that run going into next month could hardly be more difficult, with the Jambos facing matches against Motherwell, Hibs and Rangers after the Aberdeen and United games.
But former Chelsea trainee Stevenson, 25, believes Jefferies and coaches Billy Brown and Gary Locke have given the side renewed confidence about what they can achieve.
"Him, Billy and Lockey have been excellent," Stevenson said.
"He's kind of breathed a bit of fresh air into the team and long may that continue."
Stevenson had a hand in both goals yesterday but he admits he has still to produce his best form in the SPL after spending his entire professional career in the lower leagues.
"It's been difficult moving up and getting to know the players, obviously, coming from where I came from," he said.
"I'd been at Ayr for a long time, I knew the place inside out, and it's a bit strange when you come from there to Hearts, a club this size.
"I obviously wanted to get in and show what I could do as quickly as possible."
Hearts, who today revealed striker Gary Glen should be fit for Saturday's trip to Pittodrie, have struggled to score goals this season but Stevenson's arrival has co-incided with a more prolific spell.
Asked if Jefferies had given him any special instructions on that front, he said: "He's just asked me to do what I did at Ayr - that's why I'm here.
"So I'm not really trying to change anything.
"Obviously, listening to him and working with the standard of players we've got here is going to make me better.
"I want to try to get a goal as soon as possible as well to get me settled on that front."
Hamilton boss Billy Reid insisted Sunday's defeat did not dent his belief his side would avoid relegation this season.
Rock-bottom Falkirk won on Saturday to close the gap to Accies to just one point but Reid said: "We can't influence other teams.
"It's what we do and I'm always a believer in that. If it's not good enough then it won't be good enough.
"But we believe we've got good enough players here to turn this around and to start winning games and we will do that, I guarantee it."