Iran is now on the top of the points table of Group B and they are looking for a win against the former world champions to seal their spot in the round of 16.
Bilic argued that he had sympathy for Spain due to how Iran had set up defensively but former England striker Ian Wright and Keane seemed to disagree strongly with the former Hammers boss with Wright highlighting that Spain should have played better in the first-half while Keane threw his eyes to the heavens.
Carlos Queiroz's side produced a defensive masterclass to reduce Spain to nothing more than half-chances during a hugely frustrating opening 53 minutes for the 2010 champions.
Iran thought they had equalised soon after though, with Saeid Ezatolahi blasting home from close range, only for VAR to correctly chalk it off for offside.
Spain will face Morocco in its final match on Monday in Kaliningrad, while Portugal plays Iran in Saransk on the same day.
He said: "I think there are 32 great teams here at this World Cup and no-one is giving anything away, so anyone who thinks it is going to be very easy to score and win by a landslide is wrong".
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Costa was accused of standing on the foot of Iran's Ali Beiranvand.
Iran famously picked up the victory in the World Cup for the first time since 1998 against Morocco.
Iran did their utmost to frustrate the 2010 world champions in a clash of styles, but Diego Costa eventually opened the scoring with a scrappy 54th-minute victor that ended up the evening's only goal. Both the team look to have arrived in their best form for tonight.
Isco and Andres Iniesta's magic has probed the Iran defence, but a series of last ditch tackles have been enough to keep the game goalless at the Kazan Arena. Whose side are you as the Spaniards take on the Iranians?
Isco jumps on Diego Costa as they celebrate Spain's goal against Iran at the Fifa World Cup.
Iran kept a firm head on all fronts, despite David Silva's attempted volley that sailed over the crossbar after 30 minutes. Labelled the "Iranian Messi" Azmoun will be facing Spain in the familiar surroundings of the Kazan Arena.