The Uruguayan was put in behind by a long Dani Alves pass and finished clinically past Iker Casillas in the 56th minute to secure a 2-1 win for Barca on Sunday.
Cristiano Ronaldo had cancelled out Jeremy Mathieu's opener in the first half at Camp Nou, where Barca opened up a four-point lead atop La Liga.
Suarez said it was the most crucial goal of his short Barcelona career so far.
"For now it is the most important goal I have done with the club and has an extra meaning, because of the opponent," he told TV3.
"The squad is very happy."
With 10 league games remaining, Barca are well-placed atop La Liga.
But Suarez said it was important for his team to stay focused and avoid becoming complacent.
"We know that the league is very difficult," he said.
"We must seize this advantage against a very strong team like Real Madrid. As in all leagues, you never know what can happen if you relax a little."
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
