The Uruguay international netted either side of an Ivan Rakitic goal to end a run of five games without scoring and help the reigning champions secure three points.
Suarez, however, says the victory was all that mattered.
"Of course I am happy with the two goals I scored, for what they mean, but I want to make it clear that I wasn't obsessed about not scoring recently," he told Movistar.
"These are things that happen in football. The important thing is to help the team, it doesn't matter who scores the goals."
Espanyol had frustrated Barca until Suarez opened the scoring five minutes after half-time.
The 30-year-old was delighted with what he described as a "priceless" victory, sending Luis Enrique's side back to the top of LaLiga by virtue of their superior head-to-head record over Real Madrid, who have a game in hand.
"It was not an easy game at all. Espanyol came out well in the first half and were well organised in defence," said Suarez.
"We couldn't find a solution. But thanks to our intensity, desire and our ambition, we didn't give up and the goal eventually arrived and calmed us down.
"The win today was priceless, of course. We have to win everything, the three games we have left, there's nothing else. We just have to keep winning and keep the pressure on and see what happens in the end."