The two-time reigning champions met rivals Munster at the Aviva Stadium last weekend - a venue at which they had not lost in six years.
However, a blistering first-half performance from the Munstermen set them on track to end that record and they eventually completed a 34-23 win.
Defeat leaves Leinster outside the top half of the GUINNESS PRO12 table after five rounds, having picked up just two wins to date.
Next up is Italian outfit Zebre, who have downed Ulster and run the unbeaten Ospreys very close in their last two outings, and Heaslip is counting on a response from his teammates.
"It wasn't easy. I don't like losing, full-stop," said the Ireland No.8.
"Losing at home - we pride ourselves on being strong home and away and especially at home - and then to top it off losing to Munster, I hate for several different reasons.
"I felt emotionally drained sitting in the changing room, I don't know how long it took me to even take off my jersey.
"In my stubbornness I still thought we were going to pull it off but it was too little, too late. But you've got to wear it - it's as simple as that.
"I was walking the dog at five in the morning, thinking about the game, because I couldn't sleep. It eats at you. If you play a good game but you get out-performed you would walk away and think 'fair enough'.
"You did what you did, but you didn't get the outcome - but we didn't play to the standard we have set ourselves and we hold ourselves accountable for it.
"That just simply won't be good enough this week against Zebre if we're like that and it won't be good enough going forward so we have got to rectify that."
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