“I’m not interested in the speculation," he told Sky Sports. "What is likely is I’ll speak to Mel Morris the owner in the next few days when the dust settles and then we’ll see how it goes.
Lampard embraces Fikayo Tomori after the final whistle
Image credit: PA Sport
"I’ve got a two-year contract and I love working at this place. The fans giving the players an ovation, so we’ll see.”
Derby join Reading and Sheffield United in losing three second tier play-off finals - the joint highest - and focus will now turn to how the Midlands club will set about achieving promotion next season.
The manager may not be the only change, with the make-up of the squad set to be very different.
The Rams have six senior players out of contract this summer - Efe Ambrose, Craig Bryson, Ashley Cole, David Nugent, Marcus Olsson and Kelle Roos - while four loanees - Andy King, Mason Mount, Fikayo Tomori and Harry Wilson - will all return to their parent clubs.
Dean Smith leaps for joy as Lampard cuts a dejected figure
Image credit: Getty Images
Villa's local-born midfielder Jack Grealish, who was close to leaving the club before the start of the season, showed his class throughout and was delighted with promotion.
"I'm speechless. It was such a hard game. It means the world to go up, we know where this club belongs. I've stayed here and we're back there now. I've led my boyhood team to the Premier League," he said.
A 10-match winning streak during the run-in propelled Smith’s Villa side into the playoffs where they got past West Midlands rivals West Bromwich Albion in the semi-finals.
John McGinn, Jack Grealish, Dean Smith, Manager of Aston Villa and Anwar El Ghazi of Aston Villa celebrate with the trophy following victory in the Sky Bet Championship Play-off Final match between Aston Villa and Derby County at Wembley Stadium on May 27
Image credit: Eurosport
Smith, who began the season at Brentford and took over from Steve Bruce at Villa Park in October, said the club had an exciting future with the backing of owners Nassef Sawiris and Wes Edens.
"It feels very good. The lads are a terrific bunch. They take on different ideas, they deserve it. I believe pressure is what you put on yourself, we work hard every day, the only difference is expectation.
“We've got two owners have got a lot of money, and are in it for the long haul. The potential now is massive," he said.