Aitor Paredes cancelled out Artem Dovbyk's opener for Roma.
Valverde said: "It was a very hard-fought match. We started off very well in the first 15-20 minutes, but then we suffered because they pushed us back a lot. In the second half we came out with more determination, we pushed hard and that's where we got our reward.
"Matches last 90 minutes and people are always very attentive to the starting eleven, but during the game things can change. There are players who, from the bench, only act at the end, which is when the game is decided. They have given us some breathing room
"The opponent is playing and they are good. They were throwing at Dovbyk to make us delay our defensive zone, we were having trouble overcoming their markings and sometimes the messages of looking for space led us to rush. We finished the first half well and it helped us to play more freely."