Suarez, who has repeatedly denied the allegations, was also fined £40,000 after an independent regulatory commission found him guilty of abusing Evra during a Premier League match in October.
Expressing his disappointment on Twitter, Suarez said the decision had hit him hard.
"Today is a very difficult and painful day for me and my family. Thanks for all the support, I'll keep working," the 24 year-old tweeted.
He then added on his official website: "I'm upset by the accusations of racism. I can only say that I have always respected and respect everybody."
"We are all the same. I go to the field with the maximum illusion of a little child who enjoys what he does, not to create conflicts."
Liverpool, who have fully supported the Uruguayan ever since the issue came to light after the 1-1 draw, came out fighting in their response to the punishment.
And there is a feeling within Anfield that there has been a witch hunt to punish Suarez, whose defence was based on claims he was unaware language that is acceptable in Uruguay is viewed as racist in Europe.
"It appears to us that the FA were determined to bring charges against Luis Suarez, even before interviewing him at the beginning of November," said a club statement.
Suarez's manager Kenny Dalglish also used the social networking site to say: "Very disappointed with today's verdict. This is the time when @luis16suarez needs our full support. Let's not let him walk alone. KD."
Liverpool, who are awaiting the written verdict with interest, will almost certainly appeal within the 14 days they have to do so and Suarez's punishment has been suspended until that decision has been made.
It means that Suarez will be available for tonight’s Premier League game at Wigan.
Manchester United have yet to make any comment on the findings.
