The Premier League outfit, playing their third match in less than a week and without 11 injured first-teamers, fielded a barely recognisable second-string side and nearly slipped up against Exeter who are languishing in the bottom half of League Two.
Liverpool manager Juergen Klopp made 11 changes from the team that beat Stoke City in the opening leg of the League Cup semi-finals on Tuesday with Christian Benteke and forgotten man Jose Enrique, featuring for the first time in nearly a year, the only two with more than four senior appearances.
Exeter, sensing the opportunity to cause a huge upset on home turf, went ahead after nine minutes when a low cross from Jamie Reid was poked home by top scorer Tom Nichols.
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Liverpool, who have never lost in the FA Cup to a side from the fourth rung of English football, were level three minutes later when teenage striker Jerome Sinclair took advantage of hesitant defending to fire the ball home.
The hosts went back in front on the stroke of halftime when Lee Holmes caught out Liverpool keeper Adam Bogdan direct from a corner, his swirling delivery creeping under the crossbar, but left back Smith's equaliser on 73 minutes earned a replay at Anfield.
While Exeter will be looking forward to reaping the financial benefits from another meeting, Klopp could barely contain his frustration.
"I can't believe we have to play another game now," the German told the BBC.
"It's obvious what we have to learn in the future. We have to be more robust. It was a difficult pitch. Exeter did really well. On one-on-one situations they were more robust than our guys."
Exeter, who as a minor league side held Manchester United to a draw at Old Trafford before losing the replay at home in 2005, caused a young and inexperienced Liverpool plenty of problems.
The hosts missed two good chances in the first half and had strong penalty appeals turned down after the break when Christian Ribeiro went down under a challenge from Kevin Stewart.
(Reporting by Justin Palmer; Editing by Tony Jimenez)
