Appreciation is a powerful tool given to mankind. Appreciating a person for the work he/she does boosts their confidence and brings about a new meaning to their way of looking at things. It can be treated as a medium to motivate people.
It is important that we understand that motivating someone might be something of lower priority to us but it is an essential part of life. Researchers for eg physicists spend their lives working on finding a new planet for instance, seldom does someone succeed in such a mission with no direction or problem statement but appreciating them for their efforts would make them feel important. The feeling is almost as good as succeeding in your research.
Never shy away from being the one who accepts that someone is better than you at something. You need a heart of titanium to do that but believe me it shows how humble you are. You may win a competition but remember there were others who failed by an inch but tried very hard. Yes they didnt get through but atleast they tried and that is appreciable.