Coyle saw his side battle back from a goal down at Aston Villa, a ground where Bolton had conceded 13 goals in their three previous visits.
He told the Bolton News: "I was conscious Bolton did not have the best record coming here of late and I tried to make sure that didn't pray on the players' minds.
"We have to respect other teams in the Premier League but I don't want to be fearful of anybody.
"I want us to go toe to toe. We know, with the quality that some of the clubs have, it won't always go our way. But I want us to compete in every game and try to win, whether that's home or away.
"We're not trying to come and shut up shop. We're trying to impose our qualities and, for a lot of the game, we did that.
"We're progressing in the right way but are nowhere near where I want us to be. It's a work in progress."