Acknowledge your mistakes for two reasons

First, because it’s right. If you make a mistake, if you’ve had to change plans late in the game, if you hurt someone, if you say the wrong thing, swallow your pride and be honest about what you did. Its the good and right thing to do.
Second, because it actually builds trust. Many people think that acknowledging your mistakes will loose people’s trust. And to some extent, depending on the mistake you’ve made, that’s true. But that’s the effect of making a mistake.
But if people think you NEVER make mistakes, and they stop trusting you because you made one mistake… well, they probably never trusted you very much in the first place.
Most people, on the other hand, will appreciate that you told the truth. The very fact that you swallowed your pride, stood up and said, “I think I’ve made a mistake, we need to go in this direction” or “I think I’ve done the wrong thing here, I’m sorry and I wan’t to make it right”… they both have the effect of earning people’s trust, because you’re choosing to act in a trustworthy manner.