The Australian was filmed during a talk on leadership for Fuso, the Japanese parent company of England sponsors Mitsubishi.
The footage was uploaded by Fuso to YouTube in July last year but has only come to light before Saturday's final round of the 2081 Six Nations when England face Ireland at Twickenham.
In the talk, Jones told an audience: "We've played 23 Tests and have only lost one Test to the scummy Irish. I'm still dirty about that game. But we will get that back!
"We will get that back, don't worry, we have them next year at home, we will get 'em back!"
Earlier in the talk, Jones discusses Japan Under-20s losing to their Welsh counterparts 125-0 shortly after he took over as Brave Blossoms head coach in 2012.
"Wales. Who knows Wales? Are there any Welsh people here? So it's this little shit place that has got three million people. Three million!" he said.
In his apology, released by the Rugby Football Union, Jones said: "I apologise unreservedly for any offence caused - no excuses and I shouldn't have said what I did. I'm very sorry."
The Rugby Football Union added that it would apologise to the Irish and Welsh unions.
England ceded the Six Nations title that they have held for the past two years with a round to spare after losing 22-16 to France in Paris last Saturday.