Gareth Southgate’s side negotiated their way to the semi-final of the competition but were unable to overcome opponents who had played extra-time in both their previous matches.
Kieran Trippier's early free kick gave them the lead, but Ivan Perisic pushed the match into an additional period, in which Mario Mandzukic became the decisive factor.
Croatia became just the fifth team in World Cup history to have played extra-time and then overcome opponents who had not played an additional 30 minutes in their previous game.
As such, Mourinho sees this as an opportunity spurned.
“England have reason to cry because they were so close, but they also have reason to be optimistic,” he told Russia Today.
“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.”
“It's a great achievement for a country where the league is a minor league and the majority of the players don't play in Croatia but abroad,” he said.
“As I know, when you work abroad, you feel your country in a different way.
“So for them to go back to their country and take a nation like Croatia to the World Cup final is something amazing.”
Croatia have gone to extra-time in all of their knockout games and will face a France team far fresher in Moscow.
They had overcome Denmark and Russia to reach the semi-final, before eliminating the Three Lions.