The Spanish giants’ hopes of reaching the tournament final were ended by a dominant French side at MetLife Stadium.
However, the former Bayer Leverkusen coach insisted his team left the United States as a "better team," hopeful of forging a new path of growth.
Alonso told the media: "More than the distance between the two teams is the margin we have to improve. It's the end of this season and not the start of the next.
"We’ll take the positives from this Club World Cup period. We're leaving as a better team. It's a starting point for a better start next season.
"I'm talking about the team and not the players. Today, we had some shortcomings, and sometimes it's good to see the mistakes so that they can be useful for the future. If we repeat the same mistake over and over again, we won't be intelligent."
PSG have bounced back strongly after a shock group-stage loss to Brazilian side Botafogo, securing four consecutive wins to reach the final.
Their most impressive display came in the semi-finals, where they overcame Los Blancos. Luis Enrique’s side also extended their remarkable knockout streak, having now won their last five knockout matches across all competitions.
"PSG is a project created over time, and we're just starting out. It's not only because you want to be braver that you're better," Alonso added.
"There were two harsh blows, and we weren't on the pitch. We needed to relax a bit, and it was a shame to concede the third before half-time.
"We have suffered against a team that's at a good level, and we're just starting this new stage. There is a lot of margin.
"It hurts, and our level wasn't good enough. This match will show us things for the future to compete at a better level than today. This is as far as we've come. We fell at the penultimate hurdle, and it hurts.
"I thought we had to wait because in the second half, we changed the pressing from 4-3-3 to 4-4-2 with Gonzalo on the left. The analysis of the decisions will be looked at, and I'm open to criticism.
"We're all together, and this end won't mark us too much for the beginning of the next season. This will be a restart from zero, not from 98, how we have finished today."
When asked about the future for himself and his Real Madrid squad, the 43-year-old responded: "I'm leaving with a perspective for next year, when we will recover players and there will be changes.
"Next season will be different, but I'll leave with clear certainties. I take all the information that this tournament has given me. We want to build a team that plays as a unit and where everyone is involved."
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