"An awful lot of what we strive to do is about respect and you need to beat the best to get respect. And we did that tonight in beating Munster," Bradley admitted afterwards.
"One of the main things for us is that when we perform at home - I know we've lost twice here in the Magners but the performances have been excellent - the players respond very well to the crowd.
"We'd a full house today and it was a privilege to play in front of them. We'd something similar against Leinster and it makes a big difference.
"I think Munster have found that over the years, Ulster too and Leinster are currently finding it. It's a big factor.
"When we go away from home, obviously it's the reverse. There's a negative factor there. It's something we have to improve on.
"We're conscious of it but first and foremost we obviously want to play well at home in front of our home crowd."
The former Ireland scrum half, who was appointed to his current role in April 2003, had an extra bit of satisfaction in seeing Connacht turn over the European champions.
"I'm delighted and there's one very specific reason why I'm delighted. I played in the last match that Munster played against Connacht that Connacht won (back in 1986), so now that monkey's off my back!"
On a more serious note, Bradley insisted that Sunday's gritty performance from the Connacht players should go some way to ensuring that some of them gain international recognition and that playing for a team in the lower reaches of the Magners League, they can get overlooked for Ireland honours.
With Johnny O'Connor currently out injured, full-back Gavin Duffy was the only player in the Connacht matchday squad with a Ireland senior cap to his name.
"Those guys out there worked extremely hard. We kept the pressure on Munster and tried very hard to keep the positional situation correct, even though it was very difficult in the second half," Bradley added.
"We do crave involvement at international level. It's disheartening for us that we don't have enough recognition for what our players do in a side that wouldn't be a fancied side.
"Ireland need to change things in terms of the personnel when they compete at international level because the same people are going there all the time.
"We had quite a number of back-up Irish players playing against us tonight and they were well beaten.
"The questions are there for other people to answer but certainly our guys put their hands up today. We backed up the Leinster result.
"So it's up to other people to run with it in terms of picking some of our guys and giving them a chance at a higher level."