The Blues made the trip to Bramall Lane having dramatically scored two goals beyond the 99th minute to defeat Manchester United 4-3 on Thursday night.
However, Chelsea were on the receiving end of a late goal on Sunday evening as Sheffield United twice came from behind to secure a deserved share of the spoils.
Despite largely being second-best, goals from Thiago Silva and Noni Madueke had put the West Londoners on the brink of victory, only for Oli McBurnie to equalise in the 93rd minute.
Although Chelsea are on a seven-match unbeaten streak in the Premier League with 12 points to their name, they are without a clean sheet in nine top-flight fixtures and have conceded at least twice in the most recent five matches.
What did Pochettino have to say?
Such a poor defensive record means that the pressure remains on Pochettino's shoulders, and the Argentine has acknowledged that Chelsea's game management must improve if they wish to move higher up the Premier League table.
Speaking to reporters, as quoted by football.london, the Argentine said: "Very frustrating because we conceded in the first-half after we scored. Then you concede in the last few minutes, you always feel very disappointed and frustrated.
"I want to say the draw is a fair result. Even if we control and have possession, we didn't create enough. We didn't show the capacity to be solid and be strong. That is the painful situation."
He added: "The first part of the season we were a little bit more solid but were not creating as much. Now we are scoring much but conceding more. It's difficult to find the balance. We tried adapting the situation with different players and different situations on the pitch.
"The team is not showing in the last few months the capacity to be solid. We score goals but we are conceding and that is why they punish us."
Where do Chelsea go from here?
Chelsea remain in ninth position in the Premier League standings, five points adrift of sixth-placed Manchester United with a game in hand.
There is now an eight-day break before Chelsea are back in action, that fixture being a home encounter against Everton on April 15.
Following the meeting with the Toffees, Pochettino's side are faced with a succession of matches against high-profile opposition, starting with Manchester City in the FA Cup semi-finals on April 20.
Three days later, they make another trip to North London, this time to face Arsenal in the top flight, before visiting Aston Villa on April 27.