City looked like being frustrated by Eddie Howe’s side with Gabriel Jesus’s effort cancelling out Charlie Daniels’ stunning early strike before a 97th minute winner by Raheem Sterling earned Pep Guardiola’s men all three points.
Sterling was then sent off for a second yellow card by referee Mike Dean for the manner of his celebrations with the travelling City fans in a frenzied, madcap finale.
It was breathless, frantic stuff - and according to Kompany gave Bernardo, who was making his first full start and Mendy, who made his City debut, the perfect window into what makes the Premier League so special.
“Madness. The first thing I did was say to Benjamin Mendy and Bernardo Silva, ‘welcome to the Premier League’,” said Kompany.
“I thought we played well, like we did against Everton. We did not score our chances but we have big, fast, strong players and anything can happen. We deserved to win, but they made it hard for us.
“Our strength of character showed and we dealt with the physical challenge well. Overall, we won 95% of our challenges, which is a good sign.”
Kompany also gave his reaction to the Sterling dismisal, saying: “I do not know whether the crowd ran to Raheem or he ran that way. It was too many emotions to control.”
For his part Bernardo, who produced a fine display before making way for Sergio Aguero in the second half, admitted his main emotion was one of relief.
“It was a tough match for us. We did not start well but we played well after that,” aid the Portuguese midfielder.
“All the games are difficult, all the team are competitive but we got the three points.
“The manage asked me to be myself, as I did last season for Monaco. I need to get adapted to the team and I am feeling well.”