The 37-year-old Leeds man had not scored a try for almost 12 months but went over twice in the first half to help the First Utility Super League leaders to their fifth win in a row and their 20th successive victory at Salford.
It was only the second time Peacock had scored two tries for Leeds, the last coming in 2009.
Coach McDermott said: "Jamie has had a bad back and probably shouldn't have played.
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"He lasted 70 minutes and if we had taken him off after 25 or 30 minutes he would probably have seized up."
Salford's last home win against the Rhinos was a 21-12 Regal Trophy victory at The Willows in November 1993.
But their depleted side turned in a battling show, trailing 16-12 at half-time, before slipping to only their second defeat in the last eight games.
Full back Niall Evalds followed up his two-try show against Wigan with another brace with the Red Devils' other touchdown from Lama Tasi.
Peacock crossed for his side's first two tries before Ash Handley, the outstanding Rob Burrow and Zak Hardakar crossed to seal a hard-fought win in difficult conditions.
Salford, already without suspended Rangi Chase and Weller Hauraki, were shorn of another six regulars and coach Iestyn Harris said: "Our effort was really good, as was the way we defended apart from conceding a disappointing try just before half-time.
"We were a little naive with the ball but that can be down to a lot of forced personnel changes.
"We didn't quite have the fluency of Leeds which they had in key positions but we stuck with them for 80 minutes.
"Maybe a year or so ago we would have been blown away in the second half against a very good Leeds side.
"We only had 17 players available but will have George Griffin back from Wakefield this week."
Harris also hailed Evalds and said: "Niall never lets us down and is growing his reputation.
"He has the knack of being able to turn up in the right spot and that's a real asset for a full back."
McDermott added:"I wasn't really happy with what we delivered other than the result.
"We got away with a few things but the conditions were crazy. The wind had a big bearing.
"We knew we would be a down on energy after Easter but it wasn't a terrible performance and we played a little care-free in the second half.
"Jamie Peacock and Stevie Ward were massive, as was Ash Handley, and Zak Hardaker showed a lot of leadership qualities.
"But St Helens (Friday's opponents) won't be quaking in their boots the way we played."
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