Elharrar tweeted she could not attend the COP26 summit on Monday because it was not wheelchair accessible.
An official in Israeli Prime Minister Naftali Bennett's delegation confirmed they had formally complained to organisers.
Karine Elharrar tweeted that it was "sad" the UN "does not provide accessibility to its events".
Eustice told the BBC: “We deeply regret that incident.
“What would normally happen in this situation is that Israel would have communicated that they had that particular need for their minister.
“There was obviously something that went wrong in this instance and they weren’t aware of that and so they hadn’t made the right provisions at the particular entrance she was coming to.
“It’s deeply regrettable and we’ve apologised and I know James Cleverly, my colleague in Government, is going to be meeting her later.”
He faced some criticism for the remarks, with Lib Dem peer Lady Ludford tweeting: "Not the most gracious of responses for the COP26 host to blame the guest."
Ms Elharrar told BBC News she had gone into COP26 on Tuesday "very easily" and it was "quite a different experience".
"We can talk about accessibility and the rights of people with disabilities, but in life we need to implement all the conventions and all the regulations and that was an experience that showed that we need to pay attention to all the details everywhere.
"I am sure it will be different in the future."