George Ford notched a superb solo try for the English side and set up another for Stuart Hooper but the Irish province held on despite severe late pressure.
And Heaslip is convinced that his troops' greater experience told when it came to crunch time.
"We can take a lot of positives out of it," said the 31-year-old. "They're on our line, they're 25 metres out in that last minute and a half, two minutes of the game.
"But at the next level, we have a massive challenge and we've got to improve.
"We're just going to rest up now. A lot of us were saying that's probably one of the fastest, toughest games we've played, including internationals. That's right up there."
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