Mourinho said he felt "OK" about finishing second but insisted United were not celebrating their Premier League position.
The Austrian global is also determined to finish the season on a good note when West Ham host Everton on Sunday.
Mourinho is known for wanting more experienced players - and Willian of Chelsea is the one being mentioned - which in itself is not always a bad thing.
"I hope I can continue this next season".
The point means United will finish as best of the rest behind champions Manchester City while David Moyes' Hammers move within two points of the top half with a game remaining.
Speaking on Sky Sports, Redknapp said: 'If you look at the money they've spent and watch how they play... it's hard to watch at the moment.More news: Caesars Entertainment Corp Big Money Sentiment Up in Q4 2017 touching 4.4
'We needed a point to finish second, they didn't need anything because they did the job last match at Leicester but they played to win. It's the club's best league finish since they last won the title under Sir Alex Ferguson.
After admitting he "trusts some players more than others", Mourinho had his say on the speculation surrounding the future of eccentric midfielder Paul Pogba.
"I was very far from it and when I saw the reaction of the players [at full-time] I believe it was nothing extraordinary".
"We had to get the players in order a little bit after we came in, and we have done that".
'No, ' Mourinho said when asked about a potential loan for Rashford.
Declan Rice has become a mainstay in the West Ham line-up this season, having put in a number of solid displays and continued to produce that fine form Thursday night.
Of course the other reason it was hardly surprising is that it's West Ham and Manchester United and neither are playing exhilarating football right now, their apparently "traditional ways" no longer being adhered to.