"I didn't know he was there, I only found out afterwards," Beckham added.
"But he loves football and he'll go to every game possible. Obviously being in Italy over Christmas, he was able to come to this game."
After Ronaldinho had an early penalty saved, Genoa went ahead on 25 minutes but Milan were 2-1 up at half-time.
Leonardo's side ran riot in the second half to keep the gap between them and leaders Inter Milan at eight points.
It was a promising start for Beckham, who is spending a second spell at Milan in a bid to prove to Capello that he is worth a place in England's squad for the World Cup.
Beckham celebrates Milan's third goal with scorer Marco Borriello
He almost set up a goal inside five minutes, whipping in a cross from the right for Marco Borriello, who forced a superb save from Genoa keeper Marco Amelia.
And it was a trademark sweeping pass from Beckham which led to Milan's second penalty of the game, allowing Ronaldinho to make up for his earlier weak effort with an emphatic spot-kick to make it 1-1.
Thiago Silva gave Milan the lead before the break, slotting in after Ronaldinho's header had been cleared off the line.
Marco Borriello scored a superb double, the first a tap-in after a flowing move and the second an acrobatic volley to put Milan in control at 4-1 in the second half.
All that was missing for Beckham was a goal to cap his return, and he appeared to be one of the candidates to take Milan's third penalty of the game in the 74th minute - won by the excellent Ronaldinho.
However, substitute Klaas-Jan Huntelaar, who has struggled for confidence since his arrival at the San Siro, eventually took it and drove his spot-kick high into the net to complete the scoring for Milan.
A minute later, a smiling Beckham came off to a warm reception from the home fans.
"No, I didn't desperately want to take it," said Beckham of the third penalty.
"To be honest, I think it's always important that the penalty taker always takes the penalties and that's why I gave the ball back to Ronaldinho.
"But then he gave it to Klaas and he took it, but it's not important."
AC Milan are eight points behind leader Inter Milan, with a game in hand.
Jose Mourinho's side earlier ground out a 1-0 over Chievo thanks to a goal by Mario Balotelli.
But the game was overshadowed by an injury to Inter defender Cristian Chivu, who suffered a fractured skull in a clash of heads.
The Romanian spent nearly an hour in surgery to relieve a haematoma and take out bone fragments.
"Everything went normally and therefore we are quite confident the patient can recover without problems," doctor Sergio Turazzi said in a statement.
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