The bill was withdrawn on Friday because it did not have enough support to pass in Congress.
Speaking to the Washington Post, Mr Trump said "We couldn't get one Democratic vote, and we were a little bit shy, very little, but it was still a little bit shy, so we pulled it."
The last-minute retraction is seen as a huge blow to the president.
Repealing and replacing the programme known as Obamacare was one of his major election pledges.
House Speaker Paul Ryan said he and Mr Trump agreed to withdraw the vote, after it became apparent it would not get the minimum of 215 Republican votes needed.
Republicans currently have a majority in both the House and the Senate
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