Andy Robinson's side again opened the Six Nations with another deflating defeat.
Just once in 13 attempts have Scotland won on the opening weekend of the tournament since Italy joined the Five Nations in 2000 after Saturday's 13-6 loss to England.
Despite dominating much of the play, familiar failings, notably the lack of a try, proved costly.
Rennie, though, is optimistic of an improvement at the Millennium Stadium.
He said: "We're a bit down, but there are already a lot of conversations of how we can improve.
"We've got a massive game next week, it's a big challenge and everyone's looking forward to it.
"We did do enough to score tries. We made several line breaks, it's just a matter of finishing it off.
"I don't think we need to do anything very different - it's just being able to tweak it."
Edinburgh openside Rennie fully justified his selection ahead of John Barclay with a strong performance alongside David Denton and Alasdair Strokosch in the back row.
The 25-year-old almost created a try-scoring opportunity for Mike Blair, only for England full-back Ben Foden to snuff out the danger.
It was a moment Rennie rued.
He said: "I went through, I looked for my support and I saw Greig (Laidlaw) covered in English shirts.
"I looked back again and I saw Mike coming through. By the time I looked back ready to pass, Foden was in my face. It's something I'll lose sleep over."
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