Since winning the competition in 2014-15, Barca have generally disappointed in Europe's elite competition after the group phase.
Atletico Madrid, Juventus and most recently Roma have eliminated Barca at the quarter-finals stage in the last three campaigns, while they fell at the same hurdle the year before their last success in the Champions League.
But it has not been all doom and gloom for Barca, as they have won La Liga in three of the last four years, and while Pique wants an improvement in Europe, he insists they cannot afford to let that impact their form domestically.
Speaking to reporters on Monday, Pique said: "I guess it is the most important title there is for the great teams in Europe.
"[But] just to [try to] win the Champions League would be suicide. If we focus on the league more, that is the barometer which we rely on to know how good we are.
"Barca have never won the Champions League without La Liga, so let's focus on the league and win the Champions League too.
"Nothing is missing from the game of Barca. Our way of playing makes us very strong in regular competition, where many games are played, as opposed to a final, where everything can be decided by a shot or cross.
"There are teams that base everything on the counter and it can come good, but it is different to play La Liga and the Champions League.
"It has been proven that, if we work very well in the league, we are doing well in Europe. When we play at the same level [to opponents], we suffer, and when we are very superior, we are better."
Barca have started the defence of their Liga title in good form, winning both of their opening two games ahead of Sunday's clash with newly-promoted Huesca.