The Ecuador international started at right-back at Vitality Stadium as the Red Devils sealed a 3-1 victory over Bournemouth on Sunday afternoon.
Mourinho has signed Ivory Coast defender Eric Bailly, Swedish defender Zlatan Ibrahimovic, Borussia Dortmund star Henrikh Mkhitaryan and Juventus midfielder Paul Pogba in the summer transfer window.
However, former Tottenham Hotspur midfielder Crooks has tipped Valencia to play just as important a role as Mourinho’s new signings in the Premier League this season.
“Valencia was always Manchester United’s outlet against Bournemouth in a frightfully tight first half, when space was at a premium,” Crooks told BBC Sport.
“But you can always depend on him to retain the ball under pressure and he did it at a time when United needed it most.”
Crooks added: “The Ecuador international has been playing the game a long time and has served United well over the years.
“However, I suspect that for all of Mourinho’s multi-million pound signings, it is Valencia – bought by Sir Alex Ferguson seven years ago – who might well prove to be one of his most important players.”
Valencia, who has won two Premier League titles, the FA Cup and the League Cup, moved to United in a £16m deal from Wigan Athletic in 2009.
The Ecuadorian midfielder has scored 21 times in 250 appearances for United over the past seven years.
United will take on Southampton in their next Premier League game at Old Trafford on Friday night.
The Red Devils are at the top of the Premier League table ahead of Liverpool and Chelsea after Sunday’s 3-1 win against Bournemouth.
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