The 30-year-old sealed a return to Merseyside on Wednesday in a £4.5million deal having rejoined on loan in January from Tottenham.
Twelve months earlier, Pienaar swapped Goodison Park for White Hart Lane but left north London with only five league starts to his name.
A place on the periphery seems highly unlikely under Moyes, who first signed the South Africa international from Borussia Dortmund in 2007, also on an initial loan deal.
"If someone believes so much in you and shows so much respect for you as a player, for me I just have to go out and give 120 percent every week and hopefully this time around we can win silverware," said Pienaar, whose club last claimed a major honour by winning the 1995 FA Cup.
"This is the fourth time (signing for Moyes). The manager knows I am an honest person who will give my all. I think that has stuck in his mind and that is why he has so much faith in me."
Pienaar's winter arrival last term along with those of Darron Gibson and Nikita Jelavic helped to spark a surge up the table to a seventh place finish - one spot above neighbours Liverpool.
But this purple patch also shed light on Everton's unwanted tag as habitually slow starters, something Pienaar accepts and wants to get rid of.
"I think every season it is the same story with Everton," he said. "It's not only last season.
"I think it is like a glove for the club - the players tend to wake up in the second half of the season.
"But hopefully we can work towards it this season, get a good start and finish well."
A positive start may prove difficult initially when Everton kick-off the season at home to Manchester United, although Moyes' men have every right to be buoyed by the previous meeting between the sides.
United surrendered a 4-2 lead as a pulsating contest finished 4-4 at Old Trafford in April, handing the title initiative to rivals Manchester City in the process.
"It's going to be a totally different game," said Pienaar, who scored Everton's crucial fourth goal on a topsy-turvy afternoon.
"It's the beginning of the season so last season will be behind both teams.
"We just have to start well for us and hopefully we can upset them, especially at Goodison Park.
"We seem to have a quite good record against them at home. If we can start the league really good hopefully it will be a promising season for us."
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