High-flying United travel to face their fierce rivals at Anfield on Saturday looking to maintain a rich vein of form that leaves them trailing Manchester City only on goal difference at the top of the table.
Mourinho had a mixed first season at Old Trafford, finishing a disappointing sixth in the League but winning the Europa League and League Cup.
But big-money summer signings Romelu Lukaku and Nemanja Matic have impressed in the early weeks of the season, enabling United to keep pace with free-scoring City.
"I think we are a better team (than we were)," Mourinho told Sky Sports. "You can say, like some people do, we have not played one of the top five teams but last season we did not beat West Ham at home, last season we did not beat Everton at home or Southampton away.
"I think it would be unfair to say (Romelu) Lukaku and (Nemanja) Matic did not make an impact. We have to admit that and give them what they deserve.
"But also the team give Matic and Lukaku the conditions to arrive the way they have.
"Globally we are a better team. Does that mean we are going to be as successful as last season, winning two titles? I don't know. But we are better."
Mourinho, already without France midfielder Paul Pogba, shrugged off the loss of muscular midfielder Marouane Fellaini, who suffered a knee injury while on international duty for Belgium.
Asked about the Fellaini injury, Mourinho told Sky Sports: "No blow, no problem. We don't cry with injuries. We may cry with the process that leads to the injuries but we don't cry with the injuries. We just trust the players that are going to play."
United have also had concerns over the fitness of striker Lukaku, who has netted 11 times since his move from Everton, but he came off the bench and scored in Belgium's 4-0 win over Cyprus on Tuesday.
Mourinho said he was relishing the clash with Jurgen Klopp's Liverpool, who have struggled in recent weeks and are seventh in the table and have injury problems of their own, with forward Sadio Mane out for up to six weeks with a hamstring injury.
The Portuguese manager said he was relishing the trip to Anfield, where United played out a 0-0 draw last season.
"I like to play against the best teams, I like to play against the best clubs and I like to play at the best stadiums - the stadiums with more history," said Mourinho.
"At Anfield I've had great moments and I've had bad moments," he added. "They have had happiness against me, they have had very sad moments against me.
"(Now) if they respect me as much as I respect them, we are going to have another one of those matches."