Keane is upset with Solskjaer after the United boss suggested his team should not be considered Premier League title contenders.
Asked what message Solskjaer's comments sent to the dressing room, Keane replied: "It's not great. No, it's not great.
"We said it I think after the Arsenal game a few weeks ago, that we didn't have that feeling from watching the games, from that group of players.
"And obviously when Ole came up with it that he didn't feel they were ready to win the league, I just feel if you play for Man United and you're up near the top, you've got to believe you can win the league title - or what's the point being at Man United? You might as well go to a mid-table team.
"You're at Man United to win titles, it's as simple as that. I don't tolerate this idea, particularly with the position they're in. As I said, they've got goals in their team.
"But again defensively, I've been critical of them, and the goalkeeper, I'm certainly not his biggest fan.
"The one thing you want from your goalkeeper is courage - and he didn't show that for the equalising goal. Not a good sign."