What Pres. Wilson should have regretted was the poor way that he went about trying to get the Treaty of Versailles and the covenant of the League of Nations passed by the US Senate.
Pres. Wilson knew, or should have known, that there would be some major opposition in the Senate to the way that the Treaty was being written. Given that, he really ought to have taken those objections into account as he negotiated the treaty with the other world leaders. He knew that he would have to get it through the Senate, and yet he did nothing to try to make the treaty more palatable to Senators.
Historians often say that Wilson was too stubborn and arrogant. They say that he should have tried to compromise and to take into account Republican ideas when he was negotiating the treaty. His major regret should have been that he failed to do this.