Lionel Messi scored two second-half goals as last term's treble winners Barca defeated the Gunners 2-0 in the first leg of the last 16 clash at the Emirates Stadium.
Luis Enrique's men are aiming to be the first club to go back-to-back in the Champions League since AC Milan managed the feat over 25 years ago, and Suarez claims they have the quality to do so.
"We are very ambitious," the striker told reporters after the match. We want to carry on winning trophies and adding titles to this club because we are in the best team in the world.
"We just need to focus on getting our goals."
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However, Suarez remains wary of Arsenal heading into the return leg, stating the Premier League title contender's quality is not to be discounted.
"We are very happy as we got really nice score but we know that it is still not done," the Uruguay international added.
"There are another 90 minutes extra to be played.
"We know that we have taken advantage but you never know what could happen in Champions League games.
"Arsenal are fighting to win the Premier League and they have players who can make differences in the second leg."