The point saw them drop to 19th place in the Barclays Premier League table and piled the pressure on for when they play Aston Villa in one of their games in hand on Tuesday. The Trotters found themselves behind inside six minutes as Scott Sinclair curled in a beauty and, although Chris Eagles equalised eight minutes later, Swansea dominated the second half.
Coyle said: "We came here wanting the three points and we've taken one. Sometimes you've got to stand up and be counted, take that ball and be brave in possession.
He added: "We obviously gave ourselves a mountain to climb at the start, although it was a terrific finish from Sinclair. But I've showed them all week what he wants to do, he wants to come in on his right foot, and that's certainly my frustration that that's been allowed to happen.
"But the players came storming back into the game, scored a great goal, and I thought we got a grip of it, particularly towards the end of the first half.
"I thought we were well placed to go and win the game but in the second half Swansea dominated the game for 25 minutes. We allowed them far too much opportunity with the ball, and that was through giving the ball away under no duress.
"There's no doubt how hard our group work but, when we get the ball, we want to see the quality we've got. It was the wrong decision-making in the wrong areas but who's to say that won't be the point that keeps us up."
The Trotters had one golden chance but Eagles' shot from the edge of the box flew just the wrong side of the post. Anything more than a point for the hosts would have been an injustice, though, and Swansea boss Brendan Rodgers felt Bolton were lucky to get that.
He said: "We certainly deserved the three points. It was a terrific game. Of course there's a wee bit of tension around but I thought we were excellent and we created enough chances to win the game.
"We scored a very good goal to go in front early on but conceded a disappointing goal from our perspective. But the reaction to that was outstanding."