Mexican Aguirre is a former Atletico coach, himself.
"All coaches have been questioned at some stage," he said.
"Even (Barcelona coach Pep) Guardiola was on his debut in Soria (when his side lost to promoted club Numancia).
"Quique has them given two titles (the Europa League and the European Supercup) in a short space of time and that is very difficult to achieve.
"He deserves all the respect and support from the fans because I think Atletico are in very good hands."