Bradley was left frustrated after Jamie McGonigle's 95th minute strike saw his side leave Foyleside empty handed on Friday night as Derry laid down an early marker to reinforce their early season title credentials.
The 2-1 win which followed a 2-2 draw against Dundalk at Oriel Park certainly sent out a statement to their league rivals and Bradley said he wouldn't be surprised if Ruaidhri Higgins' troops had eyes on their Premier Division crown.
"I'm sure they will," he responded when asked if Derry's performance suggested they could launch a title tilt. "When you spend the money they spend you would fully expect to go and challenge for the league. They might be saying differently but they will be expecting to go and challenge to win the league.
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"We'll see. It's the second game of the season."
Bradley felt his team were in the ascendancy with the game locked at 1-1 and claimed it was an 'uncharacteristic error' from the normally reliable Roberto Lopes which cost them in the end.
"I think for the last 15 or 20 minutes we were the team pushing on and looked like we would win the game. We had the feeling they were hanging in for the last 15 or 20 but we made a mistake and to be fair to (Jamie) McGonigle, he had a lot to do and he finished it really well.
"He's (Lopes) been the best centre half in this country for the last three years and very, very rarely does he make a mistake like that. He made it tonight and we got punished but like I said he's been outstanding for us. He was good again tonight but that happens.
"Overall I thought it was a poor game. Typical start of the season game, conditions didn't help either team. First half we struggled to get out and in the second half they struggled to get out. It was a scrappy game and it looked like it had a draw written all over it. We had some half chances, they had some half chances but we have to accept we made a mistake and got punished."
Ex-Rovers midfielder Brandon Kavanagh came up against his former club for the first time since leaving to join Derry for a small fee in the close season and Bradley was impressed by his performance.
"He did well. We know Brandon has talent and he did well tonight and we wish him the best."