Everton midfielder Gareth Barry has welcomed the increased competition
Schneiderlin, 27, arrived from Manchester United in the January transfer window, while academy youngster Davies seized his chance to put in some impressive performances.
And despite greater competition for midfield places at the club, Barry has welcomed the challenge.
"At my previous clubs and in past seasons at Everton, there has always been competition for places," he told Everton's official website.
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If you are going to achieve anything then you need that competition for places
Everton midfielder Gareth Barry
"But certainly at the moment, the manager has made good signings and added players who can come in and play at any time.
"If you are going to achieve anything then you need that competition for places all over the pitch.
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"As a club we need that, and it is fantastic to come in and work knowing that you need to be on your game at all times to be in the team."
Barry continued to discuss the buzz around Goodison Park, and believes the club are capable of achieving a top-six finish.
Gareth Barry started Everton's 6-3 victory over Bournemouth
Morgan Schneiderlin joined Everton from Manchester United in January
"There are certainly comparisons to be made between the run we are in now and those we enjoyed in my first season here," he added.
"We had that great finish to the season and collected 72 points, which is a massive number.
"You get that same feeling around the club now that there was around back then. You have the young players coming through, the new signings coming in and there is an excitement around the place.
"You can feel it from the fans as well. Hopefully we can keep it going and finish the season strongly.
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"A lot of players are playing at the top of their game now and if you get a high number of them doing that and working hard then you can achieve great things.
"In the recent run, that’s what’s been happening but we know that in the Premier League it can change so quickly. We have to keep our standards and keep our levels.
"I do think you need to set yourself a little aim. If we can go on a little bit of a run and finish the season strongly then there is no reason why we can’t catch up with one of those European spots."