The introduction of Darwin Nunez in the second half brought Liverpool to life and the Uruguayan flicked home his first Premier League goal since a 75-million-euro ($77 million) move from Benfica to level.
Mitrovic restored Fulham’s lead from the penalty spot after he was tripped by Virgil van Dijk inside the area.
But Mohamed Salah ensured Liverpool at least did not start the season with a defeat by slotting into an empty net from Nunez’s pass.
“We started actually exactly the opposite way that we wanted,” said Klopp.
“We are used to more dominance and we never could get that because we just played not good enough, not quick enough, not precise enough.”
– Tottenham’s title dream –
By contrast, Tottenham had a dream start to the campaign to raise hopes they could compete for a first league title in 61 years.
Spurs also fell behind to James Ward-Prowse’s strike from the edge of the box after just 12 minutes, but the response from Antonio Conte’s men was emphatic.
The goals to turn the game around before half-time came from unlikely sources as Ryan Sessegnon and Eric Dier headed home.
Mohammed Salisu then passed the ball into his own net for a comical own goal on the hour mark.
Dejan Kulusevski rounded off the scoring with a cool and precise finish into the far corner to take Spurs above Arsenal at the top of the table.
Newcastle may not have delivered the big-name signings many expected in the transfer market, but the Magpies did the business on the pitch to spoil Nottingham Forest’s return to the English top flight with a 2-0 win.
Forest have even outspent Newcastle in the window on 12 new signings so far, but were given a lesson in the step up in quality to the Premier League at St James’ Park.
Fabian Schar’s sensational strike opened the scoring before Callum Wilson’s predatory finish sealed the three points.
Bournemouth were also 2-0 winners over Aston Villa, dispelling their pre-season gloom after a lack of transfer activity.
Jefferson Lerma got the Cherries off to a great start after just three minutes and Kieffer Moore added a second 10 minutes from time.
Leeds shrugged off the loss of Kalvin Phillips and Raphinha over the summer as they beat Wolves 2-1 at Elland Road.
Daniel Podence had fired Wolves into an early lead, but Jesse Marsch’s men fought back impressively.
Rodrigo blasted in from a narrow angle to level before Rayan Ait-Nouri’s own goal decided the game 16 minutes from time.
Chelsea begin their campaign later on Saturday away to Everton.