I am a begeinner learning the Colle system. However, I am immediately confused after facing the anti-Colle:
[FEN ""]
[startply "6"]
1. d4 d5 2. Nf3 Nf6 3. e3 Bf5
After losing the game, I learn from the engine, or the opening explorer that the 'correct' move is 4.c4. But why? What is the idea behind? Why is 4.Bd3 not as good? Also, what will be the strategy or main idea after the 4.c4 move?
That's nothing to worry about. Your opponent probably tries to build some London system structure for Black. You may confidently continue 4.Bd3. Yes, c4 gives White better chances than structures with c3 but you are not getting a negative evaluation. Your position is absolutely fine. You probably lost the game because of some mistake later on. It's not the problem with the opening. Your opening is fine. Good choice by the way because beginners and amateurs should not spend too much time on theory (openings) which variations with c4 require. That's why the London system or Colle are a smart choice. Nakamura even posted a YouTube video where he taught a beginner (Pokimane) the London system. It's not bad at all. Once again, don't worry about the evaluation that engines make calculating 15-20 moves ahead! Even grandmasters don't understand it. That's why they sometimes use lower depth when analyzing their games. If you calculate 2-3 moves ahead on average, I suggest not using analysis deeper than depth 10-12 (5-6 moves ahead) unless you are evaluating openings. In the latter case, you may want the engine to show you the best moves but even then you might be better off with ideas and plans from books or from a high rated coach/player rather than looking at the impressive depth and billions of positions calculated by the engine.