The Spaniard suffered the first serious setback of his Toffees reign with a 4-0 hammering at Anfield and, after losing a first-half goal to Leandro Bacuna, things seemed to be going against them.
The Blues, who enjoyed 71 per cent possession in the match, made their pressure pay thanks to late strikes from substitute Steven Naismith and Kevin Mirallas' stunning free-kick.
"I think it was a challenging week," Martinez told Sky Sports. "We were all very, very disappointed after Tuesday for the meaning of the result and the opposition we were playing.
"Remember, it was only our third defeat. We're all very much happy with the way things are going, but were (left) disappointed.
"In our first-half performance (against Villa) we were very cagey wanting to win the game without being ourselves, without being freed.
"We hit the post and then Villa go at the other end and score and that's a real test of character.
"That half-time moment defined our season. There is something very special about that dressing room and we showed everyone what it is in football terms, which was that second-half display."