I don't think so mate.
He came to the Prem two years ago now, and during that time there were still plenty of teams based around possession (us, the RS, Spurs (though they were getting away from that as Poch implemented his game plan), City, Utd etc.)
Koeman built on what Poch had set out and added a bit more solidity to it, so while he's in no way a pioneer he always looked to counter possession-based football with quick incisive play, while enjoying enough of the ball at the same time.
So yeh, maybe now is the time to look at how teams counter 'the press', and go in that direction. But nobody really has ever found a way to counter it. Every team gets success from it, when it's done correctly.
So yeh, we definitely need better players who are more adaptable.
My point for a few weeks now has been that we have a squad full of average to good players who are only able to play one way. That way doesn't work and hasn't for a year now.
It needs a shake up, and that is Koeman's job.
However, that being said, he wasn't ever just going to come in and overhaul the squad straight away without fully assessing it first.
In the meantime, the players need a huge kick up the arse and, to an extent, Koeman does as well to ensure that he changes things and this slump is arrested.