The Colombian international moved to the Allianz Arena on a two-year loan deal. The Bundesliga outfit have the option of signing the former AS Monaco star on a permanent transfer after his loan spell.
Chelsea signed Morata, while defender Pepe moved to Besiktas. The trio played their part in helping Zinedine Zidane's retain the Champions League and also won the La Liga in the 2016/17 season.
However, the European champions have struggled this season. Real are currently fourth in the table with 39 points after 21 games, and 19 points behind leaders Barcelona with a game in hand.
Heynckes believes Real's failure to bring in new players after allowing the likes of Rodriguez, Morata and Pepe leave in the last summer transfer window is one of the reasons for their struggles this term.
"That Madrid is going through a low in the league at the moment is, in my opinion, quite normal, especially if you have won the Champions League twice and been Spanish champions too," Heynckes told Goal.com.
"In addition, Real have given away three very good players in the summer with Alvaro Morata, Pepe and James Rodriguez, perhaps to save salaries.
"They have not bought big and thought that with the young players they can compensate for that. You need a really good mix between young and old, between experienced and hungry players."
Real are already knocked out of the Copa del Rey by Leganes and have Champions League as the realistic competition left to win this season. They have already won the Uefa Super Cup, the Spanish Super Cup and the Fifa Club World Cup so far this campaign.
Zidane's men take on Paris Saint-Germain in the Champions League round of 16. Heynckes managed Real for one season (1997/98) during which he helped the La Liga winners to Champions League glory.
He has backed his former club to progress further in the competition by beating PSG in the two-legged tie. The Bayern manager has also issued a warning to the Ligue 1 giants not to "underestimate" Real for their upcoming European fixtures.
"Nevertheless, you must not write off Real in the Champions League. They have much more experience than Paris Saint-Germain. Much more! I believe they will win the tie," he stressed.
"They have a good team for playing in European competition. When we first won the Champions League again in 1998, we finished fourth in the league. I know from personal experience Madrid should never be underestimated."