"It may have looked pretty easy, but it's really not," Alonso told reporters after his team cruised to four first-half goals to break the Dutch resistance.
He said it took Leverkusen some time to come to terms with Feyenoord's pressing game but after that "the first half was really complete."
The German giants were 4-0 up by the half-time whistle, from only five shots on goal.
"Overall it was a very serious, very efficient performance from us, but it's never easy," said Alonso, who twice lifted the Champions League trophy as a player.
Leverkusen's Dutch star Jeremie Frimpong described his homecoming as a "special game for me," adding: "We played a good first half, were dominant, and played our game."
For Feyenoord coach Brian Priske, trying to fill the shoes of former manager Arne Slot who is now in charge of Anfield, the 4-0 defeat was "not pretty."
Asked whether the drubbing showed that Feyenoord was not yet ready to step up to the Champions League, Priske conceded: "I think that's the easy and logical conclusion, yes."
"We got destroyed in four key moments in the first half. They showed the quality we of course knew they had... we had to play the perfect game," added Priske.
However, he praised his players for showing their fighting qualities in the second half, even if he admitted that Leverkusen eased off after the four-goal first-half.
"They really tried to show the supporters that we were trying to die with our boots on. But of course, we're not happy with the result," he said.
"It's definitely a hard time in this moment, but I'm a big believer that that's where you show your strength as a person and also as a player or a coach," said Priske.
"I'm going to get up tomorrow and I'm going to do everything I can to prepare the boys to be even better."
