Romero was sent off for two yellow cards before the half-hour mark as United went onto win 2-0 at Old Trafford.
Vicario said afterwards: "He is disappointed because he knows this red card could have been avoided so he apologised. He is our captain and today he made a mistake but we know the player he is and he is going to come back stronger and help us massively throughout the season."
The Italian also stated:"It is so tough. Especially when you come to play in a stadium like this one. But I am proud of my team-mates because we showed a lot of resilience and hard work throughout the game. It is tough when you are one man less to try and overturn a result that is already 1-0.
"I am proud of my team-mates, so so proud, because they put all the character and effort in today and to do it 10 v 11 is a massive reward for what we want to show for our football club, for our fans and of course the result is another defeat which is tough to accept but today - we need to take the positive that can take us into Tuesday's game."
Asked if Tottenham are now in the relegation fight, Vicario added: "It depends how you see things in life. The reality is that in terms of results we have struggled a lot. Two wins in the last 16 is not acceptable for this football club but we don't have to forget how we are trying to push ourselves in tough conditions. This is the reality.
"Of course we have had a brilliant Champions League campaign so far and playing every three games I have already played 36 games and I am proud of myself for doing this but for the outfield players it is tough, so it depends how you see things in life."