"We needed to build on that but they responded with a try almost immediately. We made a couple of mistakes which we shouldn't have made and we let them back into the game quite cheaply.
"We played well and could have gone on and won it but we were not as good at the breakdown and paid the price. We need to pick it up next week when we take on Glasgow," admitted Bradley.
"We're aware that Glasgow are playing good rugby but the fact we are at home is a big factor in our favour.
"We're frustrated by our own lack of success in the Ulster match but that was our first loss at home this season and we're want to put the record straight."
Bradley and his assistant Eric Elwood are waiting on fitness reports on a number of players - including hooker John Fogarty and lock David Gannon - before he names his matchday squad on Wednesday.
Next Friday's match at the Sportsground has been paired with the all-ticket clash the following Friday at home to Newcastle Falcons in the European Challenge Cup. A ticket to the two games will cost just €25.
"Basically, for a total of €25, supporters will be able to come to see two great games of rugby and we are all looking forward to the matches.
"Of course, season ticket holders will not need to purchase a ticket for either match and they will gain admission with their season tickets," she said.
Tickets are currently on sale from Ticketmaster and admission prices for the two games are:
Ground Ticket = €25
Enclosed = €35
Senior/Student = €20
Junior = €10
Under-7s = complimentary