Eddie Jones's side arrived in Dublin knowing that victory would seal back-to-back Grand Slams in addition to setting a new world record of 19 consecutive Test match wins.
However, Ireland smothered England to inflict a first defeat on Jones since he took over from Stuart Lancaster, and Hartley acknowledged that his side need to learn from the result.
"Big lessons to learn today. We set out to win the tournament and we've done that. Obviously disappointed not to win this final game because we had high hopes, we had high expectations of ourselves," he told ITV Sport.
"It goes to show we're not quite there yet as a team. Full credit to Ireland, [they] put us under unbelievable pressure today and gave us one hell of a Test match.
"We're not the finished article, this will keep us grounded, plenty of work to do. But full credit to Ireland today and this atmosphere was a great one to play in. I think it was negative upon negative. We seemed to back every error up with another error and they executed well."
England still won the Six Nations trophy for the second year in a row having wrapped up the tournament with victory over Scotland last weekend.