Gomes was an assured, authoritative presence alongside the combative Idrissa Gana Gueye in the middle of the park as the Toffees saw off Crystal Palace 2-0 at Goodison Park on Sunday.
The victory was the Blues’ third on the spin in the top flight as Marco Silva’s men rose to eighth in the table.
Former Benfica and Valencia star Gomes joined Everton from Barcelona on a season-long loan on transfer deadline day but saw his first appearance put on hold by a hamstring injury. The 25-year-old said he was eager to show the watching Evertonians what he was capable of – and wasted no time in displaying his class against Roy Hodgson’s side.
“It was a good feeling to make my debut - I was waiting for this moment for a long time,” he told evertontv. “I am really happy to win, I think that is the most important thing. I enjoyed it a lot.
“It was my first minutes and I want to keep improving, getting better and getting fitter.
“It was a good game. It was good for me to feel comfortable and confident. I want to keep improving day by day.
“I think the Premier League is more intense [than Spanish football]. That is the biggest difference and I am really happy to be here.
“It is really important to keep feeling fit for the next games and getting more minutes. I am working hard and now I am thinking about the next match.”
Speaking ahead of Sunday’s game, Blues boss Silva praised Gomes’ quality and mental strength, as well as his application on the training pitch.
And the Portugal international – who was a key figure for his nation as they won the European Championships in 2016 – displayed his determination and wide-ranging attributes in Everton’s triumph over Palace.
Gomes’ hunger to get on the ball was evident throughout against the Eagles – he had 75 touches and made 60 passes.
When in possession, he was both incisive and measured, finding a teammate with an impressive 91.7 per cent of his passes.
His intelligent positioning also helped thwart Palace forays forward – livewire central midfield partner Gana was the only player to make more interceptions than the Portuguese.
Gomes said the support of the Everton fans meant Goodison Park instantly felt like home.
“I felt very comfortable – the supporters were with me all the time and with the team, so I am really grateful to be here,” he said.
“It was impressive how the fans support us here. It felt really good.
“I am working to help the team. I will try to have more minutes, to feel better – and to keep winning.”
Sunday’s victory leaves Everton one point and two places ahead of next opponents Manchester United, with Gomes setting out the Blues’ resolve to rack up a fourth straight top-flight win when they take on Jose Mourinho’s side at Old Trafford on Sunday.
The midfielder believes the strong competition for places at Everton will further elevate performance levels.
He highlighted the displays of the Toffees’ substitutes against Crystal Palace – Ademola Lookman set up Dominic Calvert-Lewin to head home the opener at Goodison before Cenk Tosun rifled past Wayne Hennessey for Everton’s second – as evidence of the squad’s strength in depth.
“We have a lot of really good players, especially in the midfield,” he said. “I think it’s good for the team because we are very competitive.
“I think we want to give the manager some trouble to decide the team and the squad. Even if we bring on other players [who weren’t in starting XI], like we saw with the substitutions against Crystal Palace, we are still very strong as a team.
“We know it will now be a tough game at Old Trafford. We have time to prepare and then do our best and we hope to win the match.”