Alistair Burt spoke on Premier's News Hour after Sir Ivan Rogers announced his departure in an email which slammed the "ill-founded arguments and muddled thinking" of politicians over the country's exit from the European Union.
Mr Burt, a Conservative who backed the Remain campaign and now sits on the Select Committee on Exiting the European Union, said Sir Ivan's comments showed "point and relevance."
He said: "I hope that the good that will come out of [Sir Ivan's resignation letter] will be an understanding that what he says has real point and relevance, and it will help us as we move forward with the negotiations which will be so important to this country."
In his resignation message, Sir Ivan encouraged his civil servants to carry on challenging ministers and "speak the truth to those in power."
He added: "I hope that you will support each other in those difficult moments where you have to deliver messages that are disagreeable to those who need to hear them."
Downplaying the damage Sir Ivan's departure could spell for the UK's Brexit negotiations, Mr Burt went on to say: "I don't think any one individual is so indispensable to this process that [their departure] makes a difference.
"We will get a bad deal out of [the Brexit negotiations] if we go in, as a nation, with a very arrogant attitude that it's all about us."
Explaining the response he would like to see following Sir Ivan's departure, Mr Burt said: "What is important now is that the United Kingdom finds a united approach to the future of these very important negotiations.
"So, the prayer would be for all in government to look to close whatever gaps there may be between them personally [and] put the interests of the nation at the forefront."
Click here to listen to Alistair Burt speaking with Premier's Aaron James: