The DUP MP said those arguing to stay in the EU were raising concerns over border operations and border posts if a UK exit happened.
He also said some were arguing that Northern Ireland would "descend back into violence" if Brexit took place.
He made his comments to the Northern Ireland Affairs Committee on Monday.
It is hearing evidence about how a UK exit from the European Union could affect Northern Ireland.
The investigation comes as the EU referendum campaign begins to gather pace.
The Northern Ireland Affairs Committee is examining issues like the economy and the border with the Republic of Ireland.
In an unusual move. Gavin Robinson gave evidence to the committee on which he sits.
After hearing evidence for the first part of the session, he changed seats and was questioned by his fellow committee members.
The DUP MP criticised those who, he claimed, were using fear tactics in the referendum campaign.
"I take it pretty ill for those who suggest that Northern Ireland will descend back into violence should we not benefit from a continued relationship with the European Union," he said.
The committee also heard evidence from Ulster Unionist MLAs Michael McGimpsey and Mike Nesbitt.
The UUP leader said Northern Ireland was "a net beneficiary"  in economic terms. He argued that leaving the EU would create severe difficulties and uncertainty for farmers, the voluntary and community sector and colleges and universities.
He said the decision was "a balanced one" and said that, on balance, Northern Ireland is better remaining in the European Union.
Declan Kearney of Sinn FÃ©in told the committee: "This island's place is in Europe."
He criticised those who are campaigning for the UK to leave the EU.
He said Brexit would "reinforce partition" and would see the re-introduction of trading tariffs and customs posts.
Stephen Farry and David Ford for the Alliance Party also gave evidence. Alliance is campaigning to stay in the EU, which Mr Farry described as a "good thing ".
"The EU gives us access to a huge single market," he said.
TUV leader Jim Allister and his party colleague Henry Reilly also appeared before the committee.
Mr Allister said his party would be enthusiastically campaigning for the UK to leave the EU.
He said the EU had caused enormous damage to the local agriculture and fishing sector and the former MEP argued that it was time people were freed from the "shackles of the EU".
MPs also heard contributions from the SDLP and the Green Party. Both parties will campaign for the UK to remain within the EU.
SDLP leader Colum Eastwood told MPs that "the EU is the best example of peace-making anywhere".
He criticised those who claimed that those campaigning to stay in the EU were using fear tactics. The Foyle MLA said people  were capable of "making up their own minds".
South Belfast MP Alasdair McDonnell walked out of the meeting suddenly after he appeared to take exception to a contribution from Labour MP Kate Hoey.
During a discussion about the origins of the peace process Dr McDonnell objected to a contribution from Ms Hoey and said: "That is not acceptable" .
He said that was "the second time today" and he looked to the committee chairman Lawrence Robertson and said: "You have to control that member."
As Dr McDonnell left the room he knocked over his chair.
Ms Hoey clarified that she had not been "laughing  at John Hume" and continued to question the witness, Colum Eastwood .
East Belfast MP Gavin Robinson has warned that people are using fear tactics in the European Union referendum campaign.