Spurs pulled off a remarkable comeback on Wednesday, as they dramatically triumphed 3-2 at the Johan Cruyff ArenA to reach the Champions League final on away goals after a 3-3 aggregate draw.
Pochettino's side looked doomed after Ajax went into half-time 2-0 in Amsterdam, but Lucas Moura scored a second-half hat-trick – his third coming in the 96th minute – to send Spurs into their first European Cup final against Liverpool.
Pochettino failed to keep the tears at bay during television interviews and Mourinho, who had a difficult relationship with supporters during his time at Man United, believes the Argentine's reaction shows fans how much managers care.
"Sometimes the fans don't know how we feel, what it matters to us and the people that love us," he told beIN SPORTS in his role as a pundit.
"They don't know. Sometimes the football fans think they care more than us, they think it's just them.
"[Fans think:] 'Win a big match and enjoy, lose a match and go sad but tomorrow is another day.' Sometimes they don't know what we are like behind the scenes.
"[Coaches] are normally a very lonely person, in that football consumes a lot.
"It [Pochettino's tears] is a very beautiful way to show the world that for us managers, it means much more than for the ordinary fan, in defeat and in victory too."
Next up for Tottenham is a home clash against Everton in the Premier League, which is their final domestic fixture of the current campaign.
A win or draw will ensure Spurs finish in the top four, while fifth-placed Arsenal take in a trip to Burnley looking to close a three-point gap to their arch-rivals in the table.
Pochettino will then begin to prepare for the Champions League final, which is set to take place at Wanda Metropolitano on June 1.