United's 2-1 home win over Brentford on Monday left them third in the Premier League standings, 11 points clear of sixth-placed Brighton & Hove Albion with four games remaining.
With the top five teams qualifying for next season's Champions League, United need two more points to confirm their return to Europe's elite competition after a two-year absence.
“He's (Carrick) an amazing coach, I’ve said this many times,” striker Sesko said after scoring his 10th league goal of the season against Brentford.
"He's brought different energy. Also the way we're doing in the training, it's unbelievable and of course, I would like to have him here."
Carrick, who took charge on an interim basis in January after Ruben Amorim was sacked, has received public backing from United players including Amad Diallo and Bryan Mbeumo.
Experienced Brazilian midfielder Casemiro has scored nine Premier League goals this season, including the opener against Brentford.
"He's (Casemiro) a working machine," said Sesko. "What he's putting on the pitch is unbelievable. You need someone like this."
Manchester host arch-rivals Liverpool in the Premier League on Sunday.