Sportal.co.nz 14.May.2012Getty Images
The result proved a hard slog for the table toppers, who take on Ulster in next week's Heineken Cup final and Ospreys in a league decider on May 27.
Brian O'Driscoll (ankle) and Rob Kearney (back) are both concerns after sitting out the semi-final and knocks picked up by Eoin O'Malley, Cian Healy and Gordon D'Arcy tonight will also have to be monitored.
"Eoin doesn't look too good to be honest. He has had a pretty rough knock on the knee, so he is going off to get scanned hopefully this evening or maybe tomorrow morning," admitted Schmidt.
"We'll have more information on him then, but it is too early to tell. Cian was walking fine by the time he got to the sideline, it was as much precautionary as anything else.
"He might have a little bit of inflammation around the ankle, but that's it. I think Gordon D'Arcy just got a knock and split the top of his eye.
"I'd say after 12 years of professional rugby it's stitching on top of stitching now. It's just a case of the eye closing over a little bit.
"Your depth of perception becomes a little bit blurred so we thought that we were better off to take Gordon off and look after him for next week."
On Leinster's display, Schmidt was happy with the effort of his charges who had a 15-point haul from Jonathan Sexton and a crucial 66th-minute try from David Kearney.
"I was delighted with the effort and the endeavour. We certainly didn't hold back, I thought we defended really well for the 70 minutes until we got enough of a buffer and then we relaxed a little bit knowing that we had the game.
"Credit to Glasgow that they came back a little bit. On attack it was a really frustrating night.
"I think we got some nice line-breaks early on and didn't look after the ball particularly well which was very frustrating. I know talking to the players post-match that there was a lot of frustration around the breakdown."
Sexton booted Leinster into a 9-3 interval lead and added a fourth penalty before Shane Jennings and Isa Nacewa combined to put young winger Kearney over in the left corner.
Glasgow had defended superbly up to that point and had knocked the pre-match favourites off their stride. However, Leinster's class told and late tries for Dougie Hall and Stuart Hogg were little more than consolation for the Scots.
Sean Lineen was disappointed to bow out as Warriors' head coach on a losing note, but had plenty of praise for his players.
"They never gave up, their defensive effort on the line was outstanding. You can't keep soaking up and soaking up the tackles and it told in the end," he said.
"We will take some consolation that the guys never gave up and came back to score a couple [of tries], but as I say it was too little, too late.
"We are out [of the competition] and the guys are really disappointed there. We didn't really do it any justice in the first half and we kept giving them the ball back.
"Three lineouts and squandered throws, the scrum in the left hand corner and they pushed us off - there's four set piece attacks gone and we just didn't get enough."