Farah has been coached by Salazar at the Nike Oregon Project camp since 2011, winning six world titles in addition to the four Olympic golds.
Both Farah and Salazar deny they have ever broken anti-doping rules.
"I am firm believer in clean sport and I strongly believe that anyone who breaks the rules should be punished," Farah told the Sun.
"If Alberto had crossed the line I would be out the door but Usada has not charged him with anything. If I had ever had any reason to doubt Alberto, I would not have stood by him all this time."
Farah retired from track racing to concentrate on marathons after winning 10,000m gold and 5,000m silver at the World Championships in London in August.
He added: "I'm leaving simply because my family and I are moving back to London. We all loved spending our summer here and (Farah's wife) Tania and I realised how much we have missed spending time with our friends and family - and the kids are so happy here, too.
"We want the kids to grow up in the UK. It's the right thing to do for my family. But both Nike Oregon Project and Alberto are based in the USA, so it just would not be possible to continue our relationship from London."
Farah said new coach Lough "has an in-depth understanding of what is needed to achieve real results at marathon distance".
In July he defended his record by saying he had "never failed a blood test" after hackers Fancy Bears revealed some of his samples had initially needed further testing, before later being declared normal.