"It was hard to settle for a draw against Edinburgh because we felt we had done enough to win it. But then they will feel they could have secured victory with that late drop goal, so we will just concentrate on the positives from the game," he said.
"We did well in a lot of sectors and we will go into the Leinster match in a positive frame of mind."
Commenting more specifically on the Edinburgh game, the former Ireland scrum half added: "I thought we played very well in the second half and dominated most of it and played an awful lot of good rugby. We held our discipline, we worked on that over the last couple of weeks.
"We gave the solution to the lads in terms of shape and we were very comfortable with it so it just goes to show that these guys can go toe to toe with anybody if they have confidence in themselves, which they're gaining with every match at the moment.
"If you were to ask me before the match if I'd take two points coming off the back of three consecutive losses I would've said yes against this Edinburgh side with their internationals back.
"I thought our lineout didn't function as well as we would've liked at the start, but it finished very well in the first half and it was near perfect for the rest of the game.
"There were a lot of other facets of our game which I thought went well, our box kicking went well, our chase went well, our defensive went well, our light speed was good."
Bradley also praised the support which his side received from the majority of the 1,690-strong crowd last Friday night in Galway.
"It is crucial to us if rugby is to survive and prosper in Connacht. We need the Connacht people coming out and support us. I don't think there was any occasion, maybe one, in the last four years that the crowd didn't get value for money.
"Their participation was immense and I think it lifted the lads in particular in the second half, cheering the lads on and I think they fed off it. What we need to happen now is for them to bring a friend along next time and if we can fill the Sportsground, we can make it a very difficult place for people to come."
Meanwhile, Connacht flanker Ray Ofisa injured his calf in the draw against Edinburgh and is in a race against time to be fit for the Interprovincial clash with Leinster.
Bradley is due to confirm his squad for the Dublin tie tomorrow (Tuesday).