If I did my math right, with type coverage taken into consideration, pure Psychic-Types lose against 19 of the 26 Pokémon you fight in the league, and the remaining seven are all neutral matchups. For those keeping score at home, that's only about a 13.46% win rate (0-19-7). Dual-Types have it slightly better depending on the Pokémon- so what I mean by that is that it's basically just the Meditite family and the meteor Pokémon- but let's just focus on pure Psychic for now. Sidney and Pheobe are both self-explanatory oh-and-fivers, both of Glacia's Glalie have anti-Psychic coverage, and three of Drake's Pokémon have Crunch in this fight. Against the Champion you have your STAB resisted by Skarmory, Claydol, Aggron, and Metagross, and every Pokémon on his team has at least one physical attack. I don't have immediate numbers off the top of my head for this, but this might actually be one of the worst Pokémon Leagues for any single Type in the history of the core series. It's almost unfair how bad this League is for Psychic-Types after taking some time to look into this. But hey, at least Armaldo doesn't have any Bug-Type moves...! Yaaaaay...
The fact that the Abra family is so famously physically frail only worsens these matchups in my opinion. If Kadabra/Alakazam doesn't get OHKOs on the few targets it might actually manage to do so on, you're toast. This League tends to lean more on the physical side with most of the Pokémon you're up against and you can and will take even neutral physical hits poorly, because there's virtually no resisting any of these Pokémon. Even if Fighting-Type moves were used in this League often as a point of entry, which they aren't, I checked, the Trainer AI will just click other moves anyway if they see a KO. So, with all of this being said. Given the circumstances, I don't think you did half bad for someone that didn't know the type matchups.
Edit: Figured I'd check Wallace's Champion fight while I'm here since I'm bored and don't want to go to bed. To my surprise, Psychic actually isn't that bad here, winning against Tentacruel and going even against the remaining five Pokémon, a 53.88% win rate on a 1-0-5 record. This is a noticeable improvement from Steven's Champion fight where Psychic goes 0-4-2 for a 16.67% win rate. Notably, the Abra and Ralts families both get access to the Shock Wave TM and Gardevoir even gets the Thunderbolt TM, which can help against Wailord, Gyarados, and Milotic. As you might expect from a Water-Type specialist in an early generation, Wallace uses noticeably more special attacks than Steven's fight does, too.
