Athletic sit in 12th place on the LaLiga table, six points above the dropzone and also six points away from the European places.
Valverde, who will leave Athletic at the end of the season, said: "I'm not going to talk about 100 years ago, but when I made my debut in La Liga exactly 40 years ago, since 1986, in the Segunda División, apart from Athletic, Real Madrid, and Barcelona, everyone else has been relegated: Real Sociedad, Atlético Madrid, Villarreal, Sevilla, Valencia... We haven't.
"We have to be humble and realise that if it's happened to others, it could happen to us too. We have to keep that in mind from the very beginning of the season, and we have to understand and accept it."
Valverde also said: "Humility is not incompatible with ambition . When we at this club have all been united and pushed towards something, we can achieve incredible things.
"We're not in the position we'd like to be. We're six points above the relegation zone and six points from European qualification.
"We have to focus on what's most important for us, which is recognising that the teams below us are closing in, and having a response to that, because that's the most important thing for the club.”