The England midfielder becomes one of the highest-profile arrivals of Valencia's summer, brought in to add creativity and quality in the final third. His presentation still did not fully settle concerns around the closure of the window, with the club having failed to add a forward to increase competition in a position weakened by Umar Sadiq's injury, which is expected to keep him out for two to three months.
Elliott struck an ambitious tone despite the circumstances.
"It's difficult adapting coming from England with the rain to Spain with the sun," he said. "In the first training session, I already noticed the heat.
> "It's a big step in my career, I'm going to try to adapt to this new team, new team-mates, culture, coach. It's been a very exciting couple of days, I'm really excited to get started."
Asked about his best position, having operated primarily as a number 10 but likely to feature out wide too, Elliott said he was ready for whatever role was needed.
"Personally I'm very happy, I'm really up for playing in whatever position, with total commitment," he said. "It's been a difficult start to the season, but we have to leave the past behind, I've seen the team, the team-mates, and I'm convinced we can do things better."
On whether the club had discussed European qualification as an objective, Elliott pointed to Valencia's history.
"Valencia is seen as a great, historic club in Europe, in England," he said. "For the quality of players in the past like Silva or Villa, to name two.
"All the clubs in Spain are held in great esteem. Playing for Valencia is a great opportunity for me, to bring the team back to Europe or the Champions League. Of course it will be hard. But with hunger, with desire, with the right attitude I think it can be achieved."
Asked what convinced him to join amid the tense atmosphere following the window's close, Elliott said the decision was entirely his own.
"It was my decision," he said. "I had phone calls with the coach, where he told me the objectives and what he wanted from me. We've had difficult matches, we can't get carried away by the noise from outside. We have to go match by match, get into a positive dynamic, something that should also extend to the fans.
"I'd like it if by the end of the season we could look back on this start having achieved our objectives."
On his targets for the campaign, Elliott set a clear personal benchmark.
"I'd say between ten and twenty, that's the demand, the target I set myself between goals and assists," he said of his combined tally for the season. He also revealed goalkeeper Giorgi Mamardashvili had no idea he might end up joining until it actually happened.
"I told him I was coming to Valencia on holiday so he could give me recommendations of places to go," Elliott said. "I don't think he knew I could end up coming to Valencia until it happened."
Elliott, who will play in Mestalla's final season before Valencia's planned move to a new stadium, called it an honour to feature at a ground with such history.
"It's incredible," he said. "It's something I spoke about with my family. It's an opportunity, an achievement to be able to play matches in a stadium with so much history, where so many top-level footballers have played. It will be an honour to play here, to experience it for myself, and in the future I hope to be able to look back and remember it with pride."