The 69-year-old musician was booted from the 'Go Your Own Way' group earlier this year as the band cited disagreements over their upcoming tour, with Mike Campbell and Neil Finn stepping in to replace him.
Speaking to Rolling Stone, he said: ''Am I heartbroken about not doing another tour with Fleetwood Mac? No, because I can see that there are many other areas to look into.
''The one thing that does bother me and breaks my heart is we spent 43 years always finding a way to rise above our personal differences and our difficulties to pursue and articulate a higher truth.
''That is our legacy. That is what the songs are about. This is not the way you end something like this.''
They said in a statement: ''Lindsey Buckingham will not be performing with the band on this tour. The band wishes Lindsey all the best.''
Drummer Mick has assured fans the ''unmistakable Mac sound'' will still be on show at their concerts, which begin in June.
He said: ''Fleetwood Mac has always been about an amazing collection of songs that are performed with a unique blend of talents.
''We jammed with Mike and Neil and the chemistry really worked and let the band realise that this is the right combination to go forward with in Fleetwood Mac style.
''We know we have something new, yet it's got the unmistakable Mac sound.''
Lindsey initially joined Fleetwood Mac in 1975 before departing in 1987, but he re-joined the group in 1997.
How are the world's biggest superstars changing?
Graham J tells all about his experience with the Jazz Journal.
An interview with Nick Wilson.
He dropped his newest single Losing Sleep earlier this year.
Seven ways you can be greener at a music festival.
Listen to their song 'She Takes You Under' now.
Are you ready for festival season?
From Bastille to The Raconteurs, here's June's most exciting upcoming releases.