The Catalan giants have been eliminated at the quarter-final stage of UEFA's showpiece tournament three years in a row since going all the way in 2014-15.
Barca have lifted the La Liga title in three of the last four years, but long-serving centre-back Pique insists that it is not a case of prioritising one competition over another.
"I guess it is the most important title there is for the great teams in Europe," he told reporters. "[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."
Atletico Madrid, Juventus and most recently Roma knocked Barca out of the Champions League in 2016, 2017 and 2018 respectively.