These are situations where saying "It's just a normal" makes sense or works (most of the time):
-Experimenting with a new build pattern, position, or tactic. Bot matches should always be used before you attempt in normals, as you first need to calculate your build path, strategy, or whatever. However, bot matches can only help you get started. You're going to have to attempt in a normal match if you want to see how effective it will be in a PvP scenario. It won't always work 100% as planned, and both you and your team mates need to understand this. So if a team mate begins flaming you because it wasn't as successful as you thought, they think it won't be successful, or even if its just "breaking the meta", you can say that it is just a normal game and that you are trying to experiment with a new idea, and you're trying to work out how to use this build/tactic/position. After all, experimenting in normals is INFINITELY better than experimenting in ranked. You should still play intelligently and try to be a help to your team rather than a burden. Losing is part of the experiment, and you can use that loss to help you. Don't just make excuses.
-You aren't doing so well in lane, and a team mate begins flaming. Now, let me get something straight here. There is a HUGE difference between losing lane and feeding lane. Not every matchup will work. Sometimes, especially in blind, there isn't a way to protect yourself from being counter picked by someone else. If you've been trying your hardest not to be zoned by the enemy laner, or trying as hard as you can to keep your own jungle safe from counter junglers, and you can barely keep even with the enemy, then I think you've done fine. Some people, on the other hand, see a score like 0/2 and assume that to be heavy feeding, when it's not. If that team mate is calling you out for making them lose the game, or harassing you for the "easiest matchup to win ever", say that its a normal, and that its not the end of the world. Get help from your jungler or a team mate that's winning their lane to come up and help you. Learn why you're losing, understand what they're doing, coordinate ganks, keep your head high and don't go into tilt. You can lose lane and still come back from it and win. Don't harass other team mates for losing either, as that won't help them win in the slightest. If you win, then it was an excellent show of teamwork and perseverance. If you lose, then it was a bad matchup in a normal game. Win or lose, though, now you can learn more on how to stay even or even win against opponents like that. It's a normal game, but that doesn't mean you can't learn from it or play intelligently.
Here are some situations where saying its a normal game does not work:
-Intentionally troll picking/doing something unconventional completely unprepared. I am all for experimentation and wacky picks and ingenious tactics. But I am not for sheer randomness or stupidity. If you plan on going AD Vel'Koz jungle, PLAN AHEAD!! I don't expect you to become a god at everything you attempt, but at least have an idea of what you're doing!! When scientists do experiments, do they just run around the room throwing random chemicals into other chemicals and seeing what happens??? NO! They don't!! That's just an easy way to kill you, other scientists in the room, or everyone within a 6 mile radius! Scientists carefully calculate their procedures, they outline what they're supposed to do, and they attempt to execute it to the best of their ability. Do they work all the time? No! But was it an honest attempt that, in the end, taught them more about how something worked, and could lead them to develop something that really does work? Hopefully, yes. So don't just go Lux jungle, not know what to do or how to play your role, and then question why other people are mad at you when you use the "it's just a normal" excuse. Again, start with bots and work out a plan. Don't dive in blind without knowing what to do.
-Feeding lane or being an asshole. Remember when I said there was a difference between losing and feeding? Well, there is. I can work with you if you're merely losing lane. If you can get decent CS, or you can maintain power in the face of an "unwinnable" lane, or just generally stay as close to even as possible with the enemy, I can help you. In fact, I will help you if you need me to help you. You'd be very surprised at how easily you can turn a losing lane into a winning lane just by actually helping them. However, I draw the line at the point you are 0/5, you constantly are over-aggressive or pushing to tower, or you're being an asshole to other people for your loss. Again, I can help you, but in an ideal situation where there aren't any trolls just feeding enemy lanes, your loss is entirely due to you. Don't blame me if I come to gank and you don't engage along with me and cause me to die. If you're just losing lane, at least you're trying. If you're feeding, then you use the "Normal" excuse and continue to feed, then I'm reporting. There's a difference. Learn how to stay even, don't just give up and feed them even more. And don't rage at your jungler for not helping, because I wouldn't want to gank the 7/0 Riven and risk giving her a double kill either. Play smart. I'm okay with "losing", I'm not okay with "feeding".
TL;DR: Play intelligently, learn from your mistakes, and seek help if you need it. Don't use the "it's just a normal!" excuse soley to cover for your horrible playing.