Everton approached the closing weeks of the campaign in encouraging form after a composed 2–0 victory over Burnley. That result followed a dramatic 3–2 win away to Newcastle United, giving Moyes' side valuable momentum with just nine matches remaining.
Speaking ahead of the run-in, Moyes pointed to the improving influence of several key players who had recently returned to full fitness or form.
"We're seeing a much-improved Ili and Gana after coming back from the Africa Cup of Nations," Moyes said, referring to Iliman Ndiaye and Idrissa Gana Gueye.
The Everton manager also praised the progress of Kiernan Dewsbury-Hall, who had been working his way back following a hamstring injury.
"Kiernan Dewsbury-Hall's improving greatly because he's just beginning to get back to where he was before the hamstring injury," Moyes explained. "Getting those players back on form is helping us play better and helping us find a better rhythm."
Moyes admitted the team had needed to adjust in recent weeks following the absence of Jack Grealish, which had affected the balance of the side. However, he stressed the importance of Everton's forwards stepping up during the final weeks.
"We're still pushing the centre-forwards to try to get us goals," he said. "We need those boys, both Thierno Barry and Beto, to get us goals."
Currently sitting eighth in the table, Everton faced a difficult test next with an away trip to league leaders Arsenal.
Despite the challenge, Moyes insisted his players would approach the game with belief as they aim to finish the campaign strongly.
"Nine games to go now, and we need to keep pushing and keep going," he said. "We'll not take our foot off the pedal. We'll try to get the players in the best condition and do everything we can for the games coming up."