Buttler demands reaction from 'hurt' England as Australia loom
England went into the clash in Melbourne as strong favourites but were outplayed and lost by five runs on the DLS scoring method when rain arrived and the game was called off.
"I think we should let it hurt, to be honest," said Buttler, who is in charge of England for the first time at a major tournament following the retirement of Eoin Morgan this year.
"Days like today are really, really disappointing and you've got to feel that. There's no point in saying 'let's sweep it under the carpet and move on'.
"We have got to reflect and we have to do it quickly with another game very soon, but today should hurt."
The "character in the group is strong," he added. "I expect a reaction from the team."
The result has thrown Group 1 wide open with Australia, Sri Lanka, Ireland and England all now with one win and one loss.
New Zealand also have one win and were due to play their second match against Afghanistan later Wednesday.
It makes England's clash with Australia at the same Melbourne Cricket Ground on Friday a must-win game for both sides.
"Yes of course," Buttler said when asked if his team could handle the pressure in such a big game against the defending champions and tournament hosts.
"That's what World Cup cricket is about. Of course we wanted to go into that game having won two from two.
"In this tournament, the way it is set up, you're in must-win games the majority of the time. Friday was already a big occasion playing Australia at the MCG and even more now with both of us having lost one game."
Only the top two from each group will make it into the semi-finals.
"There's a lot of experienced cricketers in our dressing room who will have been set back at certain times in their career, so guys certainly know how to deal with the emotions of great disappointment like today."
After being sent in to bat, Ireland were all out for 157 with England reaching 105-5 in reply off 14.3 overs when the rain came.
Buttler said he wasn't upset by the umpires calling off play because of the weather.
"It was getting quite heavy, so no problem with coming off when we did," he said.
"I think the game was lost before that point. We were a long way short of where we needed to be right through the game and Ireland deserved to win."