Tries from Rob Kearney, Eoin O'Malley (two) and Gordon D'Arcy helped the defending champions take a 31-6 half-time lead, with Isaac Boss also scoring a late try in the 38-13 win.
"You don't tend to get anything easy with Glasgow, but it was certainly a relief to get through the way we did," head coach Schmidt said.
"We had to build some pretty combative phases to get over and we were just delighted to get the space on the scoreboard that took a bit of pressure off in the second half.
"The first 40 minutes was probably the best 40 we have put together. I thought we built the momentum really well and stayed really focused on the job in hand.
"Eoin (O'Malley) profited twice from that and we managed to get two others to get that bonus point which can be so important in these pools that are so competitive."
A string of second-half substitutions broke up the game's momentum and Boss's injury-time effort was the best Leinster could conjure up.
"In the second half the breakdown became a lot more muddled and there were a lot of bodies on the ground," Schmidt added.
"It was pretty messy and we didn't get the pace or continuity. We missed a couple of set pieces that worked well for us in the first half and we never got that continuity that we had in the first half."
Glasgow's five-match winning streak came to a halt in Dublin, with head coach Sean Lineen offering no excuses.
"We got well and truly spanked, didn't we?" Lineen said.
"In the first half there was only one team in it. Leinster won the contact battle hands down, both in attack and in defence.
"We talked during the week about winning the space beyond the ball but they won that battle very easily.
"It was a walk in the park in that first half and the game was over."
Following their 26-21 defeat of Bath in their pool opener, Lineen was hoping to back up that performance against Leinster, but they lacked the intensity of the hosts.
"Leinster were direct, very abrasive as we knew they were going to be," Lineen added.
"You look at four or five instances where they stripped the ball from us, like candy from a baby.
"It was men against boys at times and the guys are better than that. We played some good rugby at times, but we have found out what it's like to play the Heineken Cup champions on their doorstep.
"This is the Heineken Cup. We wanted to back up the performance against Bath and we didn't do that.
"They have got some quality players and if you don't front up against Leinster you are going to get punished, and we did."
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