The 25-year-old reached his latest milestone against Partick on Saturday.
But it is over two-and-a-half years since his one and only goal for the Leith side.
Now Stevenson says it is about time he started impressing his new manager by adding to his scoring tally.
He told Hibernian TV: "I don't know the manager knows I have only scored one goal. I might not be playing after he finds out.
"It's something I need to work on though. It's a terrible statistic but I can only get better. If I can get another I'll cut my goals-to-games ratio in half in one swoop.
"I've scored a few in pre-season games right enough - but I think that is where I peak and then it dies out after.
"But scoring more goals is my aim. I've been more positive lately because the manager has given me a licence to get forward.
"In the last three games, I've probably had more chances than I did in the 50 before it so hopefully there is more to come."
Stevenson has featured across the back four during his eight-year spell with the Edinburgh club and has been used as a midfielder in the three games under Butcher so far.
But ahead of Saturday's trip to Celtic he admits his woeful record of finding the net makes it unlikely he will ever get a chance to lead the Hibs attack.
"I've got more chance of playing in goal than up front," he said. "I will play anywhere if it gets me a game, although I've enjoyed my run in midfield lately.
"The manager has given me a chance to play in there and apart from the second half against Partick when I wasn't great, I've been doing all right.
"I know I need to perform every week because we have a great squad and there is always someone looking to take your place."
Stevenson made his Hibs debut in a League Cup tie against Ayr United back in 2005 and two years later started as Hampden as the team won the competition with 5-1 demolition job on Kilmarnock.
"I'm delighted to have made it this far," said Stevenson. "I never thought when I came here that I would make 200 appearances. It's been great.
"I have had a lot of ups and downs. There were times when I thought I'd never make 50 or 100 appearances. But to stick in and make 200 is special.
"Hopefully I've got a lot more games in me and I can stick it out for a lot longer."
There have been more lows than highs for Hibs of late following their Europa League humiliation at the hands of Malmo and consecutive Edinburgh derby defeats to administration-hit Hearts. But Stevenson sees a bright future under Butcher.
He said: "There's been some good memories and some bad ones. But I'm just looking forward. The new manager has come in and there's now a lot of positivity in the team.
"Hopefully we can now kick on and bring some more success to the club."
- Sports & Recreation
- Terry Butcher