Tapsell attracted 13,721 votes in the election and said she was humbled by the result.
"As a first-time candidate, I've had so much support. I'm grateful to every single person who put their faith in me. I'll continue to work hard over the next three years. We'll be back."
Tapsell said she wanted to acknowledge her opponents, particularly Allan and Green Party candidate Meredith Akuhata-Brown.
"It was a pleasure that the people I was up against were also strong Māori women."
Following the loss, Tapsell said she planned to thank the volunteering team in Gisborne then take the time to recharge the batteries.
"I've got an appreciation for all of the volunteers and the hard work they've put in. It's been a huge effort. We've given it our all. I'm really happy."
Outgoing MP Anne Tolley said her message for Tapsell was to "keep the faith".
"She ran a good campaign and was up against an existing MP and Kiri Allan is a good, hard-working MP. She was a good adversary for me last time but Tania did everything she could."