A first-half try by Iain Henderson and eight points from Johnny Sexton also denied them a record 19th successive Test victory.
"It just wasn't our day today," Jones said.
"Ireland played very well. It was hard to get anything going and we struggled in the line-out and we struggled in the break down. They were two key areas in a game like today.
"At the end of the day, we're back-to-back Six Nations champions. It would have been great to be Grand Slam champions and world record holders but it wasn't our day and these things happen.
"Sometimes you play against a team that's better than you and they were better than us today. They were fantastic around the break down. It was still only 13-9 at the end of the game and we didn't play well."
Ireland captain Rory Best was proud of his side as Ireland secured second spot in the championship table.
"It was a really tough game - probably when we wake up tomorrow there will be a lot of sore bodies," he said.
"They're a quality team, we knew that. You don't come here looking for back-to-back Grand Slams if you're not a good outfit.
"It wasn't something we were focusing on all week. We were trying to look at ourselves and we knew it was going to take a monumental effort to stop a team like this.
"Days like this you have to be very, very proud of the boys and the way they've fronted up against a quality outfit. They're deserved champions the way they have played this season. We're very happy with that win.
"I think we'll look back on another day at aspects of this campaign we let slip by. But that was a lot more like us. I think we can leave this championship proud of the effort that we had."