After losses to Manchester United and Everton turned the heat up on struggling Chelsea, Pochettino's side kept the critics at bay with a hard-fought success at Stamford Bridge.
Chelsea were hardly in complete control against the Premier League's bottom club, but second half goals from Cole Palmer and Nicolas Jackson sealed a much-needed victory.
"I think we talked a lot during the week after Everton about needing drastic change," Pochettino said.
"It was important to confirm that we are in a good way. The team in the first half was frustrated because we couldn't find a way past the low block of Sheffield United."
Chelsea's first goal in the 54th minute was well worked between Palmer and Raheem Sterling, whose low cross was converted with a composed finish by the former Manchester City forward.
Palmer turned creator seven minutes later as Jackson made it two, lifting the ball into the box for Sterling and Conor Gallagher to attack.
It was spilled by Blades goalkeeper Wes Foderingham and Palmer knocked it back to Jackson for 2-0.
Pochettino pointed to a change of position in the second half, swapping with Sterling to take up a more central role, as the key to the win.
"We didn't show the capacity to be flexible and it was easy for them to identify our position and to block us and make us put the ball in positions that were easy for them to stop," he said.
"The second half we were much better, we fixed things. The team started to find better possibilities to play, to link much better.
"Cole from the right, going into the space, started to link better with team-mates and be the player that we want to use - a playmaker."
Pochettino swatted aside questions about his decision to drop Argentina midfielder Enzo Fernandez.
Gallagher and Moises Caicedo featured in central midfield instead of the World Cup winner.
"You only can play 11," he said. "It's a big competition, sometimes you need one profile or another and you choose the players.
"The combination between Caicedo and Gallagher, using Cole like a number 10, that was the possibility for the best combination."
