The Basque outfit put in a better performance against the Spanish giants following their 2-1 defeat at Atletico Madrid in the previous round.
"We played a good game against Real Madrid," Valverde said. "It was a tough match and we earned a valuable point.
"My players did a good job and I thought both teams delivered good football.
"We know that in order to win we have to give 100 per cent and I expect the same determination from my players when we go to Balaidos on Monday."
Victory on Monday would see Athletic, who are fourth and hold the last Champions League qualifying spot, increase their three-points gap with nearest rivals Villarreal to six points.
Villarreal lost 4-2 at Real Madrid on Saturday.
"We know we are at an important stage in the season," Valverde said. "Every game is crucial."
Valverde has warned his players not to underestimate Celta, who are unbeaten at home since November 9.
The Galician outfit has collected 13 points of a possible 15 at Balaidos since.
"Celta have grown strong in recent months when playing at home," Valverde said. "They have obtained good results and we will have to work hard to bring home three points."
Celta followed their 4-2 triumph over Betis with a 2-1 win at Granada last time out.
The outcome lifted Celta to 11th place, five points clear of the drop zone.
Celta, coached by Luis Enrique, know they will have to be at their very best to upset Athletic.
"Athletic is one of the best teams in the league," Celta forward Nolito said. "They have very good players and it will be an attractive but very difficult game.
"We have to show the same hunger we have displayed at home recently and go out determined to take three points.
"We have the capacity to beat Athletic or any other team provided we play the way we know."