Mr Kawczynski met with the town's Conservative Association, which made it plain that it would not tolerate such behaviour.
The MP was forced to made a public apology in the House of Commons for the way he spoke to the staff when he struggled with IT and was unable to access a meeting.
After failing in an appeal against the decision to make him apologise, Mr Kawczynski said that he had reflected on his behaviour and accepted it constituted bullying.
The Shrewsbury and Atcham Conservative Association said it had since met with the MP.
A statement from the association said: "We have left him in no doubt that his recent behaviour falls short of the values and standards that all Shrewsbury and Atcham constituents should expect from their MP.
"We cannot, nor will not, tolerate bullying, harassment, or any form of intimidation. Mr Kawczynski has been strongly reminded of his responsibilities as a representative of Shrewsbury and Atcham Conservative Association and that any and all actions he takes must be to the highest moral and ethical standards."
Speaking in the Commons, Mr Kawczynski said: "I did not swear nor raise my voice but my behaviour led to two complaints. I have reflected on my behaviour, I accept it constituted bullying and as such was highly inexcusable.
"The circumstances were stressful for the staff who were assisting the committee and for me.
"I've apologised to them before and I apologise to them again and to the House unreservedly. I will never repeat such behaviour."
The disciplinary report said the politician acted in a "threatening and intimidating manner" towards the complainants after he was unable to join a committee hearing due to technical problems.
It said he had consumed a "significant amount of alcohol" on the day and phoned the manager of the committee staff while under the influence, behaviour that was "grossly unprofessional".
The incident occurred in April 2020, as Parliament was adapting to new remote working during the coronavirus lockdown.
Sir Stephen Irwin, chairman of The Independent Expert Panel which determines appeals and sanctions in bullying cases, said: "We accept that the circumstances which arose on April 27 2020 were difficult.
"But they were difficult for everyone. While we fully grasp that the life of an MP can be highly pressurised, these responsibilities and stresses do not justify a loss of courtesy, an exaggerated sense of importance or entitlement, or bullying."