The visitors would have been good value for a draw after dominating much of the second period, but Kelechi Iheanacho deflected home Yaya Toure’s shot in injury time to secure the points for the hosts.
Now the Blues have another nine days to recharge their batteries before travelling to Arsenal.
“Without the last two minutes of the match, I think 1-0 would be the perfect game for us,” said the boss. “It’s important to keep clean sheet but it’s also important for the team to win this kind of game.
I knew this would be difficult because we played in the week and we were not 100 per cent in terms of recovery.
“I think that we showed the spirit of this team when we were drawing 1-1. We knew we weren’t playing that well but we also knew we had to find another goal and fortunately, we did.”
Pellegrini also paid tribute to Yaya Toure’s display, adding: “Yaya was one of the best players in this game. He was the player who tried to create different things.
“He just came back from an injury in his calf and he played in midweek and today so I’m happy for him.
“That was our fifth game in 15 days, it was important to win this game - now we’ll see what happens at the top of the table. We have the week to work before we play Arsenal.”
