"I woke up on Monday morning and couldn't believe we were top of the table," admitted Strange, following the 16-14 triumph at Newcastle.
"When you see clubs like Leicester and Wasps below your team, it is tremendous. But we know there is a hell of a hard season ahead, and Gloucester this weekend will be a huge game.
"Maybe Bath were complacent against us, and maybe Newcastle were as well, but teams will see us at the top now and won't be complacent any more.
"We are keeping our feet on the ground, because we have only won two out of 22 and still have another 20 games to go. We are riding it for the moment - and loving it, though!"
Strange, a 31-year-old journeyman whose rugby travels have taken him to Bristol via Ebbw Vale, Llanelli, Newport and Rotherham, has played a pivotal role in his team reaching the Premiership summit.
Going into Sunday's Memorial Stadium clash against west country neighbours Gloucester, Strange has yet to miss a kick at goal this term, a record matched only by Wasps full-back Mark van Gisbergen.
"I have always had a lot of confidence in my own ability, and I feel that if I am left to run the team on the pitch and I am given some games to do it, then I can do a good job," he added.
"When Bristol were in League One last season and I was calling the shots, it did me the world of good.
"I am enjoying myself, not only on the field, but off it as well. I have always played my best rugby when I have been happy off the field."
Strange could have his work cut out playing on the front-foot on Sunday, given the immense power of Gloucester's pack and the fact Bristol are without injured international forwards Mark Regan and Gareth Llewellyn.
They will provide the biggest test yet of Bristol's resurgence, with Gloucester further boosted by their England centre Mike Tindall being declared fit after suffering a hip injury against Sale Sharks last weekend.