The Catalan coach was expected to bowl into his job at Manchester City previous year and walk away with the Premier League title after the success he achieved with both Barcelona and Bayern Munich.
He said: "Last season we were favourites too and finished 15 points behind and, from my experience as a manager, always in the beginning of the season, the new teams are the toughest ones".
It was one of the costliest moves in Europe during a summer transfer window that has seen United midfielder Paul Pogba replaced as the most expensive player in football by Neymar, who joined Paris Saint-Germain for 222 million euros ($262 million).
United will kick off their Premier League season against West Ham at Old Trafford on Sunday, with Mourinho suggesting his side can win the league.
"Midfield players scoring goals, wingers scoring goals, central defenders good in the air scoring goals at set-pieces. But we have players and if we can not strengthen the team in these areas, we have players that we trust".
Mourinho does not necessarily buy into the idea that more goals are needed, just a fairer spread to help them win more matches. In July, they sealed a £75m deal to bring Romleu Lukaku in from Everton with Nemanja Matic arriving from Chelsea at the end of the month. Naturally, a few names spring to mind, but the only thing we can guarantee at this stage is that whoever this player is, their boss is not going to be happy.
"There's no relation between clubs and countries and seasons and periods, so obviously there is no guarantee".
"It's not just hope it's convinced that the quality of the team will be better, I have conditions to deliver a better one than the first".
The 35-year-old, who scored 28 goals for United last season, has been at the club during his rehabilitation and Mourinho said the Swede could feature in the second half of the season.
Lacazette comes to Arsenal with a big reputation after netting more than 20 league goals in each of the past three seasons with French side Lyon.
I'm naturally a pessimistic person, so I head into this season with reservations about how the team will do. Not playing on Thursday nights will also be a benefit as United look to improve their Premier League form after a disappointing sixth-place finish. With the strikers we have - Sergio (Aguero), Raheem (Sterling), Gabriel (Jesus), Bernardo Silva - all of them, they're so young so they're going to stay for the future. The Europa League not the Champions League.
'You know he's injured, he needs time to recover, he's not ready to play tomorrow, ' said Mourinho.
"We have had a better pre-season than previous year and we have the confidence levels of a team that has won a European competition and returned to the Champions League".