The eagerly-anticipated Champions League last-16 tie is finely poised at 1-1 after a first leg in which Madrid dominated possession but United missed numerous chances to take a lead back to Old Trafford for the return in three weeks' time.
The visitors went ahead through Welbeck's 20th-minute header but Cristiano Ronaldo levelled matters 10 minutes later.
On the Welbeck goal, captain-for-the-night Ramos said: "He got the better of me but it was not a corner in the first place, that is certain. The margin for error in the Champions League is tiny."
Madrid boss Jose Mourinho also suggested an individual error had cost the nine-time champions, telling reporters: "If you see it on television you can see what happened.
"We train, we organise ourselves, we define each player's role, look at the videos to get to know our opponents' strengths at set pieces, but when you lose individual battles there is no level of organisation that can stop it."
Despite the setback, Madrid responded well with Ronaldo's leveller followed by long spells of domination.
But with United goalkeeper David De Gea in wonderful form they could not find a second goal, the former Atletico Madrid man making stunning stops to deny Fabio Coentrao and Sami Khedira, while a trademark Ronaldo free-kick whistled inches over the top.
Despite the fact United had even better opportunities to snatch it - Robin van Persie hitting the bar and seeing a mis-hit volley cleared off the line - Ramos remains confident Madrid can win in Manchester and advance to the quarter-finals.
"We know that we can win at Old Trafford," he said. "We dominated and had a great attitude and the result would have been different if we were more clinical.
We would have liked to go there with another result but it was not to be."
"The team had a great match despite having lots of chances that we couldn't capitalise on. I have a bittersweet feeling but that's football. There are days that they go in and others that they don't.
"I'll take away with me the great attitude of all our players. We will go with the same mentality, believing that we can win. We realise that we have to go there to win, but we know that Manchester United are a great team and must be respected."
When asked if he felt a draw was a fair result, Mourinho said: "It doesn't exist. In football, only the result counts and nothing else. We could have scored more goals and they would have been deserved if we had done."
"Despite being a little out of context with the football that they played, they also had clear chances and could have won. The expectations and excitement are high for the second leg."