Wanderers went ahead in the 64th minute through Johan Elmander but were denied victory by James Morrison's equaliser with 12 minutes of normal time remaining.
It was the fifth draw Bolton have recorded in their seven Barclays Premier League games so far this season and Coyle wants his side to finish opponents off.
"It was two teams being very positive, but for ourselves, we have drawn a game we could have won," Coyle said.
"We have lost only one game in the Premier League to Arsenal in controversial circumstances, so there is so much to be pleased about.
"But what we have to do is start turning those draws into wins and that will see us really catapulting up the table."
Wanderers midfielders Martin Petrov and Matt Taylor were amongst those who failed to make the most of goalscoring opportunities at the Hawthorns.
Coyle claimed the visitors' cause was also not helped by a poor decision from the referee's assistant, who he believed had failed to see that Baggies frontman Peter Odemwingie was in an offside position when he received the ball to cross for Morrison's leveller.
"You have to accept that you can't take every chance you get in football, but we are looking to take a percentage and we certainly created enough chances," Coyle said.
"(West Brom goalkeeper) Scott Carson made one or two saves and there was one cleared off the line.
"Sometimes you need that little bounce of the ball and that break as well, and again, you need decisions to go your way and to be given properly."
Elmander's goal was his fourth of the campaign and Coyle paid tribute to the recent improvement shown by the Sweden striker, who is linking well with 33-year-old skipper Kevin Davies - a player the Wanderers boss feels still deserves a chance to show what he could do in an England shirt.
"He knows the demands I place on him and I like to think we have helped him along the way," Coyle said of Elmander.
"But the person who deserves the biggest credit in this is Johan, because when he crosses the white line, he has to deliver.
"I think he is fortunate as well that he is playing with such a terrific leader of the line in Kevin Davies, and I am very fortunate to have him as my captain.
"For fear of being repetitive - I don't pick England squads and some people might say he is too old, but I think he would be a breath of fresh air and could bring a completely different dimension and facet to the play if required.
"But I just think they look like a real good partnership. Every time we go up the park now - as opposed to when I came in last season, inheriting a team in the bottom three which was very fragile - I think we look a real goal threat, and long may that continue."
West Brom, who have been relegated from the top flight three times over the last decade, have now taken 11 points from an impressive start to the campaign and remain in sixth place.
Last week the Baggies caused arguably the shock of the season to date with a 3-2 victory at Arsenal, but Albion boss Roberto Di Matteo insists the team's current standing is not beyond what he might have hoped.
"I wouldn't say it has exceeded my expectations," said Di Matteo, who confirmed that Jerome Thomas had missed the Bolton game with an injury he picked up against Arsenal.
"I just look at the big picture, and we have played seven games and we have 31 to go.
"We are pleased with what we have, but the main aim this season is to change the reputation of the club."
Source: Team Talk
Source: Team Talk