The former Argentina international believes the midfielder and Angel Di Maria represented a team ethos which has now been lost
The 32-year-old left the Santiago Bernabeu for Bayern Munich towards the end of the transfer window after seeing his first-team spot come under threat following the arrivals of Toni Kroos and James Rodriguez.
Valdano - who has been a player, coach and sporting director for los Blancos - believes the team have lost an important worth ethic following the sales of Alonso to Bayern and Angel Di Maria to Manchester United.
"Xabi Alonso was a much-needed player at Real Madrid due to his positioning and sacrifice," he told Cadena SER.
"He is a very intelligent player and gives the feeling that he handles the rest of the team like a herd.
"Xabi Alonso and Di Maria represented consistency, the thinking of the collective - one through his intelligence and one through his intensity."
Madrid suffered a 4-2 shock defeat to Real Sociedad on Sunday and face a vital La Liga match against champions Atletico Madrid after the international break.