Holgate played every minute of Everton's final seven games of the campaign and was important figure in the Blues retaining their top-flight status.
The 25-year-old explained how Lampard's encouragement and infectious positivity provided a foundation for him to perform.
“To be honest, I've not felt that level of confidence in me for a long time," Holgate told the club's website.
“I would never criticise anyone who has been here before, they worked hard and made the decisions they thought were best for the team.
“But it goes back to those big parts of my time here when I've gone into games thinking, 'If I don't get a clean sheet or play out of my skin, I won't play next week'.
“It is hard for anybody to go in with that mindset. It's been a bit more relaxed with this manager, I can play my game, and, hopefully, keep doing well for the team.
“I feel I have had more support to show what I can do – and consistently playing games in my position is a huge help because I can get settled and know what I am doing.
“The manager openly says he has faith in the way we are as a group and how good we are as footballers.
“You want the confidence to know you can play – if you make a mistake, you know he won't think, 'That's it, he's not good enough to do this'.
“Mistakes happen. If you're a footballer or a builder, you will make mistakes.
"If you make a mistake building, you are not a bad builder, you have made one mistake on one day.
“To have a manager who believes in you and, if you make a mistake, says, 'Keep going, keep going', rather than, 'Don't do that', is a breath of fresh air and gives us the confidence to try things."