Everton drew 1-1 at Accrington, with Beto scoring the visitors' goal from the penalty spot.
Keane told evertontv afterwards: "We played some decent stuff. I think in the final third we can get sharper, but the lads have worked really hard for 10 days straight – even yesterday we had double sessions, so it's not easy. You don't feel fresh and at your best but that's what pre-season is for. We got through it and we'll feel better for it.
"(The start to pre-season) has been really good. It's been hard work with triple sessions pretty much every day. That's going to be good for us.
"Obviously, the manager knows exactly what he's doing and we're feeling better day by day.
"For me, to play at 90 minutes tonight is good. I think a lot of lads will feel better for that and we just keep building into the start of the season now."
On the new season and new stadium, Keane also insisted: "It'll be something that's really exciting and something I think the Club deserves. I think the fans deserve it.
"The past few seasons have been tough and the fans deserve some positivity. The Premier League is a tough league and there's a lot of good teams spending a lot of money. Nothing is guaranteed but we've got to aim high – and why not?"