The actress, who has played the Time Lord since 2017, announced in July she will be leaving the BBC sci-fi drama following the upcoming series and a trio of specials next year.
Showrunner Chris Chibnall is also set to leave the programme to be replaced by Russell T Davies, who was behind the 2005 revival of the show.
Speaking during an online Q&A, Whittaker addressed the emotions she felt over her departure.
The 39-year-old said: "You have to honour the show and to honour everything. Me and Chris, there was this thing of like, 'We want to do three seasons'. But no-one holds you to that so there was always a conversation, it was always fluid. But when you commit to that decision.
"This Doctor is Chris's Doctor so for me it is right, but if everyone comes up to you forever going, 'I'm a Doctor Who fan' then that is an absolute joy because it has been such a pleasure.
"But it is also letting go of it. It will be very... I feel like I will be filled with a lot of grief for it because I kind of... Even thinking about it, it makes me upset. But this show needs new energy.
"The Doctor, the joy of this part is you hand on your boots - and you hand them on. And I don't know who, but whoever that is, what a thing to go, 'You are going to have a right time'."
Whittaker, who previously starred as grieving mother Beth Latimer in Broadchurch, recalled crying during one of her final days on set.
She said: "You know what I'm like - I'm a crier. I had to do my final (backstage interview) today. We haven't finished filming so I can avoid the thoughts a bit more.
"But obviously with the behind-the-scenes stuff, it was in that slightly concluding way and, 'Can you tell us how you feel about the crew?' and then I just lost it.
"I was just crying my eyes out, absolutely gone. I always knew this is the best time I will ever have on a job. I have felt like that from the start of it."
It was also announced that Rochenda Sandall, who played villain Lisa McQueen in BBC drama Line Of Duty, and Sam Spruell from The North Water will be joining the cast as guest stars.
Ripper Street star Craige Els, Steve Oram from The End Of The F****** World, The One actress Nadia Albina and Jonathan Watson of Two Doors Down will also feature.
It was previously announced Robert Bathurst, Thaddea Graham and Blake Harrison would be appearing in the upcoming series.
The first special will air on New Year's Day 2022, the second will be later in the spring and the third, when the Doctor will regenerate, will air in autumn 2022 and will form part of the BBC's centenary celebrations.
The new series of Doctor Who begins on October 31.