The 25-year-old Uruguay forward was handed the suspension and a £40,000 fine in December after being found guilty of racially abusing United defender Patrice Evra in a Barclays Premier League match.
"People at Liverpool are sure that it was a way that Manchester United used to put me out of the team and stop Liverpool. In England, Manchester United's political power is strong and you must respect that and shut your mouth," he told Uruguayan television show RR.Gol.
The controversy was re-ignited in February when Suarez seemingly refused Evra's handshake as the teams conducted their traditional pre-match greeting.
Suarez claims his actions were misunderstood. He said: "In England, it was shown the moment when I passed in front of him, but they didn't see that he had his hand low before. Only the media in Uruguay and Spain showed that I wanted to shake his hand.
"Previously, I had promised my wife, the manager and the directors that I was going to shake hands with Evra. There was a chance for the teams not to shake hands like in a game between QPR and Chelsea [following the Anton Ferdinand-John Terry racism row], but I told them I was to shake hands with him.
"'Why not?', I thought, because I had no problems with him. I had been punished because of him, but I had no problems with shaking hands."
Speaking at length about the subject for the first time, Suarez reflected on a difficult period in his career.
"The trial [disciplinary hearing] was so complicated for me," he said. "I had to go to Manchester in a taxi for the trial. I got up at seven in the morning and I came home at nine at night.
"I was exhausted, I was so tired. I wanted to cry, and kick all the things around me. I came home and I wanted to do all that, but I couldn't because my daughter was at home. There were really complicated days, and then things became harder after the punishment."