The Reds have been comfortably outspent by their rivals so far in the summer transfer market with Victor Munoz and Jeremy Jacquet the only new arrivals at Anfield.
However, fan confidence in Iraola remains high, after the Spaniard delivered three seasons of consistent progress at Bournemouth before making the move to replace Arne Slot in June.
Iraola is expected to make more signings before the transfer window closes at the end of August - with the club currently working on a loan deal for Barcelona defender Ronald Araujo - and Reds legend Ian Rush has full faith in the new boss.
"The first four or five games will be important. If you start well, that gives everyone the confidence to go on and be more successful.
"Winning the league is always the standard at Liverpool. Iraola has to be given time. If we win a trophy that'd be great, but if he's given time, I'm sure he will deliver the goods.
"We've got players coming back from injury so, if we can get them back fit, it might be OK. There are still a few weeks to go, so let's see what happens in terms of transfers."