Madrid brushed Juventus aside 4-1 in Cardiff on Saturday, claiming the Champions League for the third time in four seasons, while pipping Barca to La Liga's crown secured Madrid's first Liga-European Cup double since 1958.
Manchester City boss Guardiola won the Champions League twice at Barcelona, an achievement that has been matched by Madrid coach Zinedine Zidane, but the Catalan backed his former club to recover under Luis Enrique's successor Valverde.
"I congratulate Real Madrid because they were the worthy winners of the Champions League," Guardiola said at a Johan Cruyff Foundation golf day on Monday.
"But I would also tell them not to become overconfident, because Barcelona always bounce back.
"[Valverde] is a very good coach and a good friend. Barcelona have made a good choice."
Zidane has claimed five titles in his 17 months in charge at Real Madrid and Guardiola lavished praise on the Frenchman for the work he has done at the Santiago Bernabeu in turning around the club after a disastrous spell under Rafael Benitez.
"He is a great coach and, as a player, he was on another level," Guardiola said. "I am happy for him because he has done an excellent job."