Romelu Lukaku had the chance to give United the lead shortly before half-time after David de Gea stunningly denied Joel Matip in the first half.
But United, who headed into the match with 21 goals in seven Premier League outings this season, failed to function as any kind of attacking force after the interval, while Liverpool were frustrated by the disciplined defensive ranks before them.
Mourinho is without midfielders Paul Pogba and Marouane Fellaini to long-term injuries and felt he could not readjust to compete with Jordan Henderson, Emre Can and Giorginio Wijnaldum in that area of the field.
"I was feeling that I need my bench but we had no bench," Mourinho told Sky Sports, having left Spain playmaker Juan Mata as an unused substitute and introduced an extra defender in Victor Lindelof during stoppage time.
"I need to play against their three – Henderson, Can and Wijnaldum - with power and energy and we had no power and energy.
"I had [Ander] Herrera and [Nemanja] Matic and no-one on the bench to make a difference.
"If I have solutions on the bench then I can do things like I did before in the victories at Swansea and Southampton."
England duo Jesse Lingard and Marcus Rashford came on to little effect, the latter having dropped to the bench after returning from international duty with a knock.
Far from thinking the attention should be focused on his own tactics, Mourinho felt opposite number Jurgen Klopp should come under scrutiny for making his first changes 11 minutes from time and merely using Daniel Sturridge, Alex Oxlade-Chamberlain and Dominic Solanke as straight replacements for his front three or Philippe Coutinho, Mohamed Salah and Roberto Firmino.
"I know that for you and the experts it's easy to speak," he added.
"Liverpool's midfield is really strong and they never changed. They are faster than us and I had no chance to bring the game in another direction."