A champion manages to win also losing, for example learning by its mistakes.A champion is the person that after a loss is ready for next round.
Think like a champion!

Yes such examples are trophys that everyone caries with him/her at every level of chess competition.. Playing for a championship or a higher cause it increase the pressure and make your achievement looks even greater but in reality it's the same attitude with someone who finds the courage to turn a game in a simple blitz event while being a Queen down.
It's not your hunt for the title that gives you strength but your mentality to be uncompromised with any defeat. Some people have this kind of character more than others from the day they born, before even understand the world.
Personally I don't want to be a chess champion. I prefer to enjoy chess with my own pace. Sometimes I will find the courage to win/turn a difficult position, sometimes not.

I find I have a difficult time reengaging in the game if I drop a piece. Are there any resources to help fighting back when you are down material?

Well, it depends on your position. Sometimes you can sacrifice material even for initiative's sake and it's ok. Other times maybe there are some pieces your opponent doesn't use at all so your disadvantage is not visible. Yet if you just drop a piece with no compensation try to complicate the position and counterattack, use at best what you've got left. Your opponent might relax thinking he will win anyway and underestimate your offensive plan so chances are you can regain the control of your game and why not, even become the dominant party. Have fun!

Well, it depends on your position. Sometimes you can sacrifice material even for initiative's sake and it's ok. Other times maybe there are some pieces your opponent doesn't use at all so your disadvantage is not visible. Yet if you just drop a piece with no compensation try to complicate the position and counterattack, use at best what you've got left. Your opponent might relax thinking he will win anyway and underestimate your offensive plan so chances are you can regain the control of your game and why not, even become the dominant party. Have fun!
That's an interesting alternative.

Well, when I drop a piece I bluff threats and try for tactical tricks, hoping the opponent won't see them. If you play "properly" after you drop a piece, you'll lose because the opponent won't make mistakes easily.
Also, if you have some compensation for a dropped piece, like a pawn majority, oftentimes it can be useful as well to play with whatever compensation you have instead of trying to trick your way back into the game. So it depends on that as well.
When we think of a champion we tend to imagine someone who has it all together, we picture a genius who cannot fail. But the fact is champions too make mistakes. Some smaller, others bigger. Obviously we all desire to act perfectly all the time, to lead the game flawlessly. Nevertheless there are dozens of factors that can influence a game, some of which pass us by leaving our awareness dormant. What I am trying to say is that it is not all up to us and there can be circumstances out of our control. The important thing is to remember one of the principles of success discovered by Napoleon Hill which states that 'every adversity, every failure, every heartbreak, carries with it the seed of an equal or greater benefit'. When we do mistakes we should try to remedy the course of the game without rehearsing over and over the error on the display of our mind. That only leaves us with a bitter taste while wasting the energy necessary to the rebuilding process. It reminds me of my first National Championships, when I was almost ten. In the last round I was only one draw away from the champion title. I led a nice game but at a certain point I made a mistake, consequently losing a pawn. At first I became angry with myself and discouragement tried to install but I made a choice and it was the good one. I thought that I could not turn back time and also that a flower doesn't make the spring so I decided to do my best from that time on. The right attitude led to right behavior, I started dominating my opponent and won a piece shortly after that. The result was the most desired one: I won the game and I became champion for the first time! That inspiring thought and that decision at the turning point of the game facilitated my victory! (Blog article from https://camiciobanu.wixsite.com/chess-for-fun/single-post/2017/01/31/Think-like-a-champion) Hope you find it useful, please share your own thoughts on the theme, champion's style!