Was it a mistake to kill my players’ characters in our first ever combat-session?

So I’ve gathered a few friends to finally play DnD together, and after a great session zero and a smaller session one as an introduction, we met up yesterday to continue playing where we left off. As a first-time DM, I decided it would be wiser to use an adventure called “The Fouled Stream”, which I found in the Dungeon Masters Guide , instead of creating an own one. This way, I could spend more prep time rereading and memorizing the rules, so I could explain them if needed. Ultimately, I was the only one who read the rules, so it was a good choice to do so, and the adventure did go smoothly. I even found a reasonable way to incorporate the newcomer Barbarian into the adventure. My little party then bravely fought the Twig Blights, and Bullywug Warriors, while the shrieker fungus was replaced by a fey - I explained that the Paladin stepped onto something in the darkness, and without hesitation the Barbarian exclaimed that it must have been a fey. And since the barscene in session 1, where I introduced “Dodka” and “Dägermeister” as drinks served to them, everything had to start with a “D”, so the fey was quickly named “Dinkerbell”. 
Up until now, my players spammed long rests, but at the same time they complained, that fights felt a bit repetitive and too easy. By now, they didn’t even set up someone for watch during night anymore. So I improvised and decided to make them fail their next long rest by making a brown bear appear. This way, I thought, they would realize, that camping in the woods every night isn’t always safe. Since they didn’t have all their hit points anymore, I didn’t want them to get the surprised condition, so they woke up to the bear’s loud noises, and rolled a 19 and a nat 20 on Initiative, while the bear rolled a 5. Even so, they weren’t able to bloody the bear, and I thought showing off multi-attack would make them flee and think of new a strategy. So I launched an attack against the barbarian, expecting an average dice roll, but suddenly I one-hitted the Barbarian, dealing 27 points of damage, which was enough to instantly kill him. The Paladin then missed his attack, and got killed too, even though I took the smallest possible attack the bear could make- if I made the bear leave, they wouldn’t have felt satisfied, so I thought that the Paladin could instead avenge his friend and then find a way to revive him. So now both were dead and the Players were upset, and I was just as upset as them, since nothing went as planned.
Luckily, after a short break, I explained to them, that they got revived by Borogrove, a treant from session 1, who was the guardian of the forest and an npc they really loved last time. After remembering all the pain they went through during their death, I even awarded them with resistance to psychic damage, as they have experienced great traumata enough to withstand such attacks to a certain extent. Afterwards they beat the remaining monsters in the cave, cleansed the stream and made their way back home, encountering Borogrove, who slept in the bear’s fur, hung up between two trees like a hammock. When woken up, he took the fur and used it as a cloak. That was a fun moment, since my players started to idolize Borogrove. They even sat down on the train of it, and Borogrove just continued striding through the forest as if nothing happened. In the end, they got a staff of flowers and 50 gold pieces as a reward for the adventure. 

Even though it all got sorted out in the end, and they said they had fun, the mood dropped drastically after their death, and they roleplayed less. It felt harder to dive into the rest of the story for both them and me. That’s why I would love to hear some advice on what I could improve in the future, and what mistakes I made, since I would really love to keep playing DnD with my friends. 

First, I like the way you resolved it, and I hope they appreciate their Treant friend even more.

As for "mistake" eh the dice can do Some Things. A brown bear is CR 1 so it's hard to say if that was obviously too much without knowing your player character levels. If you only have two players, remember that a typical encounter is balanced for 4 and that a huge part of combat balancing is about the action economy. The odds that two players will miss in a round are much higher than the odds that four players will miss. At low levels it's easy to accidentally one-hit a character with a crit, especially if they're squishy or not at full health.

When figuring out an encounter, I try to validate what a crit looks like, and how bad it would be. Sometimes I even do a little test play if there are features I'm not sure about.

In the moment, to die is a big shock and not a surprise that the mood is changed. But, I would hope that your players will come rejuvenated to the next session. If not, having a chat with them is always the best way. Make sure you teach them and telegraph to them that running is always an option - honestly new players especially won't always think of that.