The Trotters overcame the sending off of Jaaskelainen to recover from a two-goal deficit and claim a point in a fiery Premier League contest at the Reebok Stadium.
The Finn was dismissed after 37 minutes for appearing to slap Birmingham's first goalscorer Roger Johnson in the face.
Without him Bolton fell further behind as Craig Gardner grabbed Blues' second but a Kevin Davies penalty and a stunning free-kick from Robbie Blake netted a point.
Coyle said: "I'm not going to make excuses for him - Jussi is a grown man and he has been a top-class keeper all his days in the Premier League.
"He was beside himself at the end of the game but our strength has always been in the group.
"Jussi saved us at West Ham last week time upon time, he made a great penalty save.
"We know all the squad can be called upon, we all have a part to play.
"It summed it up when Robbie Blake stepped up and fired a great free-kick.
"Obviously Jussi will be thanking Robbie this week but as a group we were thanking Jussi last week.
"That's the way it is. He made a mistake but what matters is, whether you are 18 or 35, you learn from it."
Coyle felt a point was the least his 10-man side deserved for their spirited comeback.
He said: "At 2-0 down you think it is one of those days but I have always stressed I am trying to foster and build a spirit here.
"Hopefully that was evident for everybody. I think we carried the fight.
"I think anybody at that game would have struggled to recognise it was 11 v 10 as we were the team pushing on. We were certainly deserving of a point, minimum.
"Alex may have been disappointed with the penalty but last week at Upton Park a penalty was given against us.
"It was expertly finished by the skipper and then Robbie Blake's come up with a wonder finish in the top corner.
"I had two magnificent years at Burnley with Robbie. I would have loved to have got him earlier in his career.
"We got him here to do a job and he has come up trumps."
McLeish was indeed disappointed with the award of the penalty and also thought the free-kick from which Blake scored came from a dubious decision.
The Blues boss said: "It feels like a defeat but in the grand scheme of things we believe it could be a good point.
"We are quite sore about it and the manner in which we lost the goals.
"The penalty I felt was extremely soft. It is a man's game, English football is passionate, fast, intense.
"If we are going to see penalties hopefully they are going to be consistent and see the way our guys get barged in the box.
"It would be good if he [Friend] watched it and explained why there was a penalty and why there was a free-kick.
"But good for Bolton, good fighting spirit. They never gave up and we needed a third goal to put them away.
"They are always going to be dangerous with their route-one way. Maybe we sat a little bit deep."
McLeish is now considering whether to attempt to strengthen his squad before Tuesday's transfer deadline having pulled out of a deal for Wigan's Charles N'Zogbia.
Blues were unable to agree personal terms with the French winger after agreeing a club record £9million fee.
McLeish said: "We pushed the boat out to get N'Zogbia but there are not a lot of £9million players out there ready and able to come to us in 48 hours.
"We've lost out on some good players but I think the fans need to know that we are in the market for improving the quality of the squad.
"It is going to be nip and tuck until five or six o'clock, whenever the office is shut."
McLeish also said a knee injury to Sebastian Larsson, who limped off in the second half, was not as bad as first feared.
He said: "We thought it might have been a dislocated kneecap, something severe, but it doesn't seem as bad as when he first fell on the ground."