Kieran Trippier's early free kick sent England ahead on the night, but Ivan Perisic levelled the scores before Mario Mandzukic came up with an extra-time winner for Croatia, who will face France in Sunday's final.
England managed to reach the final four of a World Cup for the first time since 1990, and Mourinho has insisted that there is plenty for the country to be positive about moving forward.
"England have reason to cry because they were so close to [reaching the World Cup final], but they have also have reason to be optimistic," Mourinho told RT.
"The team improved a lot in relation to previous appearances. It's a young team, the majority of the players will play in the next World Cup with more experience at club level.
"If I was in charge of the FA there would be no doubt that I would keep Gareth Southgate and Steve Holland in their jobs and give them the chance to take the team to the next Euros and the next World Cup.
"The players and the squad, everybody involved in the World Cup, have a reason to come back home with pride after giving everything and making the country proud."
England will now take on Belgium on Saturday afternoon for the right to finish third in the tournament.