"Yes, I was worried because you play against these teams that defend really well and then you are losing 1-0 in the first minutes, after working the whole week not to suffer those kinds of goals," Pellegrini told Sky Sports News at full time.
"The most important thing was our application to win this game. I was sure if we continued playing that we would score those goals. The best thing the team did tonight was we kept calm, we continued moving and creating space.
"It's important to win. If we lose this game, that's another consequence - it's very important. We need to continue working and I hope on Saturday we can have our first victory in the Premier League."
The third-round draw for the EFL Cup will take place on Thursday night from 7pm.