The double Olympic champion clocked the fastest time in the world this year, winning in seven minutes 34.66 seconds
"The crowd have been amazing, as has the support I have got for the last few months," Farah, 32, told BBC Sport.
He was running in England for the first time since allegations of doping were made against coach Alberto Salazar.
Salazar denies the claims while Farah himself is not accused of any wrongdoing.
Briton Farah withdrew from June's Diamond League meeting in Birmingham following the accusations against his coach, stating he was "emotionally and physically drained", but went on to win the 5,000m race in Lausanne earlier this month.
He was given generous applause from the crowd inside the arena when his name was announced at the start and the Somalia-born athlete responded with a smile and his trademark 'Mobot' gesture.
Having celebrated wildly when winning in Switzerland, he showcased Usain Bolt's celebratory pose after the finish line, in homage to the Jamaican who won the 100m event.
"I was pleased with tonight," added Farah. "I felt a bit tired at the start but you have to win the race and not to think about the time.
"You can only do what you do best. For me, that is running. It is great for the people to understand and support me.
"It was great memories from 2012 and I saw Usain Bolt win before me. We take it for granted what he does, to come out year after year and keep winning medals."
Farah took the lead after the 2,000m mark, controlling the pace of the race, and he opened up a comfortable gap before sprinting the last 200m in 26.5secs.
Britain's Mo Farah received a raucous reception as he eased to victory in the 3,000m at the Anniversary Games in the Olympic Stadium, London.