The 34-year-old was brought to the Premier League by Sir Alex Ferguson in 2003, but was sold to the Toffees after falling out of favour at Old Trafford.
"When I look back on my career in a few years, when it's all said and done, then David Moyes will have had the biggest influence on my career," the Daily Mail quotes Howard as saying.
"He trusted me a lot but, with that trust and responsibility, I sometimes got the short end of the stick. The main thing is I always appreciated his honesty.
"He gave me the opportunities that some people would never have given me. I have played hundreds of games for Everton and there are probably a few where I shouldn't have been selected, but he trusted me to keep going. I love him."
Moyes left Goodison Park after 11 years in charge to succeed Ferguson at United.