Moyes was first asked about the club's January transfer window business and if he is happy with who he was able to bring in.
“It could have been much better but everyone connected with Everton is aware of our situation," said Moyes.
"We’re feeling much better. In the future, there’s a greater chance we could be more competitive in the market. We’d have liked to have done a bit more if we could have but either prices or availability played it’s part."
The Toffees boss was specifically asked about new addition Carlos Alcaraz and revealed that he thinks he can slot right into his side.
“He’s ready to play, he looks match fit but the biggest thing to do is get him used to group the players, getting him in and not under too much pressure, he’s got Premier League experience so the speed of the game shouldn’t shock him too much."
Everton have won three games in a row under Moyes which he says is important to bringing fans together before they depart Goodison Park for good.
“We’ve probably only got eight or nine games left at Goodison forever so quite rightly so they should enjoy it and embrace it," he said.
"You get the feeling the supporters and players are beginning to get a connection back together.
"For a club like ours, ‘The People's Club’, you need the players and supporters all working together."
He then moved on to balancing the league and the cup and admitted he would love to lift silverware with the club.
"Let’s not kid everyone on, the biggest importance is to be a Premier League club, but every Everton supporter wants another trip to Wembley and a chance to win a trophy so we have to give the supporters that."
"But our position is the overriding thing, we have to retain our Premier League status."
Moyes then spoke on their excellent form and how it has lifted the club’s confidence.
“It feels great that we’ve won three games, I can sense it in the building, in the training with the players gaining confidence and a lot more self-belief. We’ve got to keep it going, we’re a long way off the team I hope we can have in the future."
The Everton boss also spoke on this weekend’s opponents Bournemouth and praised their campaign so far.
"Bournemouth and their manager are doing a brilliant job. I think they've played so, so well this season.
"We've got to hope we can get a result. The two results against them this season, it didn't go our way, so let's see if we can do it in the Cup. It's a tough game."
Finally, he opened up on Harrison Armstrong’s loan to Derby County.
"It's just the start for him and we can hope that, if he can get 10 or 12 games, then by the summer, we'll see how he's looking then."