Everton relieved the Dutchman of his post on Monday in the wake of the 5-2 defeat to Arsenal at Goodison Park on Sunday.
The defeat left the Toffees in the bottom three at the quarter way stage of the season and despite being publicly backed recently, Koeman was sacked following unprecedented spending in the summer window.
Speculation had been rife over Koeman's future for much of the season with just two Premier League wins from nine games so far.
Koeman spent over £150 million in the summer, although the splurge was offset by the loss of star man Romelu Lukaku to Manchester United for over £75 million.
The former Southampton boss was desperate to add another striker to his ranks before the window closed and was instead left with too many number 10s and no out and out forward to call on.
Now Glenn Hoddle - who like Koeman used to manage Southampton - has delivered his verdict, admitting he is disappointed by the Dutchman's sacking.
"Another one gone!" Hoddle said on Twitter.
"Just no patience anymore! Personally I think Ronald Koeman would have done a good job given time, proved that at Saints."
Another one gone !! Just no patience anymore ! Personally I think RK would have done a good job given time, proved that at Saints.— Glenn Hoddle (@GlennHoddle) October 23, 2017
Koeman became the third Premier League manager to lose his job this season following the sacking of Frank de Boer and Craig Shakespeare before him while Slaven Bilic is under intense pressure at West Ham.
David Unsworth will take temporary charge at Goodison Park following Koeman's sacking and Burnley boss Sean Dyche has been installed as the early favourite to replace him.