The Reds booked their place in the Champions League quarter-finals on Tuesday night after a 5-0 aggregate win against FC Porto at Anfield.
Tottenham Hotspur welcomed Juventus to Wembley on Wednesday night following a dramatic 2-2 draw with the Serie A champions last month.
Harry Kane broke the deadlock at the home of English football before goals from Gonzalo Higuain and Paulo Dybala secured a 2-1 upset.
Tottenham are still waiting to win their first trophy under Pochettino despite finishing in second and third place in the last two seasons.
The Argentinian coach has fallen short of silverware since taking over the reins at Tottenham from Tim Sherwood in 2014.
Liverpool FC lost to Manchester City and Sevilla in the League Cup and Europa League finals under Klopp in the 2015-16 campaign.
The Reds are challenging Manchester United for a second-placed finish in the Premier League table this term.
Former Arsenal defender Keown believes Pochettino is under more pressure to win a trophy than Klopp.
“Liverpool are a club renowned for winning trophies but they have not won any silverware since the League Cup in 2012,” Keown told the Daily Mail.
“Jurgen Klopp has made Liverpool much better than local rivals Everton and now they are going toe-to-toe with Manchester United to become the second-best team in the country.
“The fact that they are on an even keel with United may have relieved some of the pressure to win a trophy.
“Pep Guardiola described Tottenham as the ‘Harry Kane team’ and while Spurs have plenty of other fine players, there is a feeling that the club would change significantly should the striker leave.
“For that reason, there is a pressure on Tottenham to win silverware.”
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