Pellegrino pleased with important win
The victory ensured the La Liga side remained top of Group F, although it is still very much a three-horse race with Bayern Munich and the Belarusians.
With Bayern so impressive in a 6-1 win over Lille, the hard-fought victory over BATE represents a valuable three points for Valencia.
"We have taken a very good step," Pellegrino told reporters after the game,
"We played like a serious team, in a game that was more difficult than people expected it to be."
A Sofiane Feghouli double, combined with goals from Jonas and Roberto Soldado, ultimately resulted in a win that sees Valencia go three points clear of BATE.
Valencia looked comfortable at 3-0 but conceded two goals before the home crowd helped inspire Pellegrino's charges to regain the momentum.
"The fans pushed us on a lot, giving us heat and propping us up in the difficult moments,” the 41-year-old said.
"Hopefully we will continue in this direction. The match here against Bayern will be (like) a final."