The 24-year-old struggled for regular playing time at the Spanish capital club last season as they went on to win the Champions League and the La Liga. Despite the restricted playing time, he managed to score 20 goals across all competitions.
Morata was wanted by Jose Mourinho and Old Trafford and IBTimes UK earlier revealed United's interest in the striker. The Premier League giants failed to reach an agreement with Real for Morata, which was confirmed by the Red Devils manager.
Herrera expressed his disappointment after Morata failed to complete a switch to England this summer.
"Of course I wanted to have Morata as a teammate, he was very close because the two clubs negotiated. Too bad he is not with us but I wish him well," Herrera was quoted as saying by the Spanish publication Marca.
Morata will have his chance of facing United on two occasions in less than a month. Mourinho's side face Real in a friendly fixture in the International Champions Cup in the United States and in a competitive fixture in the Uefa Super Cup on 8 August.
United made it to the Super Cup after winning the Europa League and the success in the second tier European competition helped them return to the Champions League. Herrera is aware that Real are the "most powerful team" at the moment and is motivated to face Zinedine Zidane's side..
"Madrid are the most powerful team of the moment. They have won the last two Champions Leagues but a Super Cup final always motivates me," the former Athletic Bilbao man explained.
"I am just as motivated, of course, playing against Madrid and it's a good test for us. Getting back into the Champions League was fundamental to the club because we are going to be one of the rivals to beat. We are a strong team with a winning coach."
United's failure in signing Morata saw them beat Chelsea in securing the services of Romleu Lukaku. The Belgium striker moved to Old Trafford from Everton on a £75m ($96.7m) deal as he became Mourinho's second signing of the summer.
The Spain international is now a transfer target for the Blues manager Antonio Conte. However, Morata does not see Conte's side as an option and is ready to continue at Real, claims Spanish radio station Onda Cero.