Tottenham boss Sherwood laid into his team after the 4-0 humiliation at Chelsea last weekend saying there was "a lack of character" - but ex-Spurs striker Gary Lineker said such public condemnation of the squad was "unwise".
Mills, the former London 2012 Olympics deputy chairman who is a non-executive director at Tottenham, said Sherwood had every right to feel emotional at the display.
Mills told Press Association Sport: "We were playing well at Chelsea and we made some silly mistakes and we got thrashed 4-0, it happens.
"Inevitably when things don't go well the media are very keen to have inquests but if you are not prepared to take the rough with the smooth then you shouldn't be involved with football.
"He was very emotional and upset and if I had his job I would probably be emotional and upset. When he got back to the training ground I am sure he would have sat down with the players and analysed where it went wrong and try to find a way to make sure it doesn't happen again.
"This the cut and thrust and excitement of match-day but his job is to manage the team and that means understanding how each week we can improve.
"We think he is doing a great job, the results since he took over have been good and he knows like every player on the pitch that success is based on performance. He will be in a great place if we do well and if we don't he won't, the same for every player in every football club in the world."
Speaking at the Sport Pro Live conference in London, Mills said that the Spurs players had to work to cut out the kind of errors that saw Chelsea capitalise to critical effect.
He added: "The Premier League is one of the most competitive sports leagues in the world with vast amount of money spent on the teams and the players and you can't afford to make too many mistakes.
"In most sports it is the teams or the athletes that make the fewest mistakes that wins.
"Last weekend we made too many mistakes."
Mills admitted that this was a "transition year" for Tottenham with so many new players arriving in the summer as Spurs splashed out on the huge transfer fee received from Gareth Bale's move to Real Madrid.
He said: "When you bring a lot of new players as we did in the summer, several players from all over the world it takes them a long time - and longer than we would probably like - to settle in together and in the Premier League. Many had not played in the Premier League before and it is a very different experience.
"I'd like to think the vast majority of the players we brought in will develop and stay and produce the value we believe they had when we bought them.
"This year is probably for us a transition year with a large number of new players and the manager's job is to make the best of it."