Thursday's goalless draw away to West Ham ensured United cannot be caught on the last weekend of the season, despite following up Friday's 1-0 loss at Brighton and Hove Albion by drawing another blank in front of goal.
United sit 19 points behind rivals and runaway champions Manchester City - who also won the EFL Cup - and Mourinho feels his team could have performed better over the season.
"We are the second-best team in the Premier League, a fantastic competition with lots of good teams, with six teams trying to finish first," Mourinho told BBC Sport.
"We came second. I am not totally happy, that is not my nature. But since the moment we felt it was impossible to finish first we had the target to finish second and it is done today.
"I am not critical of the performance at all. Against Brighton, at half-time I told the players they were going to lose and tonight at half-time I said we would win.
"I was wrong but we were positive in the game. In the 80th minute we know that a point was enough so we start thinking about that and we let the game go."
19 - Since Sir Alex Ferguson retired at the end of the 2012-13 season, no Premier League team has drawn more matches nil-nil than Manchester United (19, level with Southampton). Dull.— OptaJoe (@OptaJoe) May 10, 2018
With second spot in the bag, Mourinho is setting a new target for United's last game of the Premier League season at home against Watford on Sunday.
"Now we have the objective to finish with more than 80 points," Mourinho added.
"It is normal that Michael Carrick is captain at Old Trafford for the last game of his career.
"David de Gea will be rested, it gives a chance for Sergio Romero to play. I can make changes."
Former United boss David Moyes was pleased with West Ham's display, even though they achieved their primary objective by securing Premier League survival last weekend.
"A point against Manchester United any time is a good result and the attitude was good," Moyes told Sky Sports.
"The players went about it really well, with a great attitude and commitment. We wanted to win and we want to move up the league if we can, but it's a good extra point.
"It's been a big achievement for us but I've enjoyed it. They're a big club with big expectations and they're looking to improve over the year, they don't want to be flirting with relegation."
Of his expiring contract, Moyes added: "We'll have a chat next week and we'll see."