Deadline-day signings Eddie Nketiah and Maxence Lacroix both made their Eagles debuts at Selhurst Park, where Jamie Vardy opened the scoring for the visitors in the 21st minute.
The Foxes were leading 2-0 thanks to Stephy Mavididi’s strike less than a minute after the restart before Jean-Philippe Mateta scored a goal and a stoppage-time penalty to draw the sides level.
Glasner said: “We saw what we knew. It’s not that we can say we play against Leicester and it’s automatically three points.
“We can also see in the results, in this round in the Premier League you always have to play on your top level.
“It was OK. Many parts of the game are OK. It’s a draw, so it’s our job that we play better, that we are more consistent in defence, that we concede fewer goals, and then we will get the win and I will be really happy.
“We have to invest to create chances and score goals, and sometimes how easily we gave them their goals.
“That says there’s a discrepancy, and this is what we all feel.
“But this comeback quality, this great impact from the subs, shows that we have a great group again and we will work hard to go from OK football to good football and then to excellent football.”
Glasner had before Saturday’s contest compared his overhauled squad to an F1 car with a new wheel, and in the first half they looked very much like they are still searching for the right gear.
They gave the ball away in midfield, allowing Vardy to latch onto Wilfred Ndidi’s ensuing delivery, and the 37-year-old outpaced Marc Guehi before rounding Dean Henderson and firing home the opener.
The Foxes made it two 23 seconds after the restart when James Justin’s cross deflected off Nathaniel Clyne, allowing Mavididi to volley home from Ndidi’s cut-back.
Mateta converted Tyrick Mitchell’s cross at the near post after 47 minutes and VAR overturned the initial offside call.
Just as it looked Palace were doomed to their third loss of the new campaign, Conor Coady sent his fellow substitute flying and Mateta converted.
Steve Cooper admitted the result felt like a defeat, revealing he had requested clarity on the VAR decision after the contest.
The Leicester boss, who remained upbeat about his side’s defensive effort in particular, said: “I thought we were really good in the first half to come away to a ground and a team like Palace and play like we did.
“Any chances that (Palace) were having, they were from difficult areas, and they were going wide and would have been difficult opportunities to score, so then to give the penalty away, you know, as we did, because we were in good position, you know, it’s frustrating.
“I’ve got to be really clear. I want to see the absolute offside image of the first goal.
“And if it is (onside) no problem, we’ll hold our hands up. But we can’t be making offsides on suggestions, which is only what we’ve seen at the moment. So we need to, we need to get that image quickly off the Premier League.
“And like I said, if it is, it is, I’ll accept it. But at the moment, and all my colleagues out there have asked the same question.”