Spurs striker Jermain Defoe equalised just past the hour and midfielder Tom Huddlestone had a chance to win it from the penalty spot after Sam Ricketts had handled from Peter Crouch but Jussi Jaaskelainen saved.
"It was a fantastic cup tie with numerous opportunities," said Coyle.
"Harry said to me at full-time he thought it was a game of two halves but I think it was a game of an hour for us with the last half-hour going to Tottenham.
"There is a lot to be pleased about. For large periods of the game we were in the ascendancy.
"If we had come in at half-time with a bigger lead no-one would have thought it was unjust.
"The players will tell you I had a blast at them at full-time because I believe we should have done enough earlier on to have won the game.
"While accepting at 1-1, with Jussi making the penalty save, we still carried a threat going forward.
"Probably none of us wanted a replay but we are in the draw for the next round and whose to say we can't go there and win the replay.
"I would hope any team I am ever in charge of you would see they would want to win every game they play in and they showed that today."
Coyle felt the penalty award may have been harsh but was not prepared to make an issue of it.
"I can understand why it was given because, if it was at the other end, I would probably be looking for it," he added.
"It is easy to look back in slow motion and see Sam's arms were already up because of the nature of Crouch's movement but the referee called it and you have to get on with it."
Coyle also revealed he hoped there would be better news on centre-back Gary Cahill, currently sidelined after suffering a blood clot in his arm, in the next fortnight.
"We don't want to get ahead of ourselves but the clot has dissolved and we'll revisit it in two weeks with a scan with a top specialist in that field," said the Scot.
"Having done that we will see what the picture is from there but there should be some news in two weeks and hopefully it will be of the better variety."
Tottenham assistant manager Joe Jordan also felt Spurs did enough in the final half-hour to have already booked their place in the quarter-final.
"The second half put us in a position where I think we should have won the game," he said.
"We lived dangerously in the first half as we didn't play particularly well and the performance was not good enough.
"But in the second half we got ourselves sorted out and we should be going away with the victory, no question of that.
"We certainly didn't play in the first half and in the first 30 minutes Bolton's style of play caused us problems and it could have
resulted in a second goal and we couldn't have had any complaints.
"It wasn't until the second half we dominated the game."
Jordan bemoaned the club's fortunes from the penalty spot but did not apportion blame to Huddlestone.
"We have not been too lucky with penalties. Normally when you see Tom take them in training he does it with power - today he tried to place it.
"But I think when a penalty is saved you have to give credit to the goalkeeper."