The former Chelsea trainee, 25, put the ball on a plate for David Obua to nod home the opener just past the hour mark and produced the crossfield ball that Brian Easton inexplicably lobbed over his own goalkeeper for David Templeton to poke home.
But Stevenson claimed it was another below-par display in his third appearance for the Jambos.
"I've been disappointed with the way I've played, I can do a lot better than what I'm doing," he said. "But, at the end of the day, it's going to take me a wee while to get used to the players, the players used to me, used to the stadium.
"I'm used to playing in front of 1,500 people; it's obviously a big step up for me to come here and play every second week.
"It was important for me to either try to get a goal or get involved in the goals.
"So I'm happy I managed to help the team."
Templeton was credited with Hearts' second goal after beating the hapless Easton in a chase for the goalbound ball.
Asked if the young striker had claimed what is his first goal for the club, Stevenson joked: "I was actually too tired to catch up with the play.
"I was just grateful that it actually went in in the end.
"But I imagine he will be because, if it was me, I would."
Stevenson believes staying patient against stubborn opponents was the key to Hearts' second straight win, which cemented their place in the top six.
He said of Hamilton: "I think, when they go away from home, they kind of sit in and they try to frustrate - they're very good at that.
"So it was about being patient and not maybe trying to force the ball.
"I think, once we got the first goal, that kind of settled us.
"When it's nothing each, you're always a bit wary that they might catch you on the counter-attack.
"So, once we got the first goal, we were able to play a bit more and get the second.
"At the end there, we could maybe have had two or three more."
Hamilton boss Billy Reid refused to criticise Easton for his error or Flavio Paixao for shooting too close to Marian Kello while the game was still goalless.
But Reid does believe his side missed absent strikers Mickael Antoine-Curier and Dougie Imrie.
"I'm not wanting to make that an excuse but the bottom line is Mickael Antoine-Curier's our top goalscorer," said Reid, whose side are only a point above rock-bottom Falkirk.
"Any team in the Premier League misses their top goalscorer.
"Big Imrie's been brilliant, he's played a couple of games for us and he's been exceptional.
"They're probably our two main forwards, we missed the two of them.
"They'll be back in the next couple of weeks, then we'll be stronger again."
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Source: Team Talk