The absence of star turn Cristiano Ronaldo gave Manuel Pellegrini’s side a great opportunity to take a first-leg lead on Tuesday, yet they were made to sweat for a goalless draw on their first ever semi-final appearance.
Jese hit the crossbar as Real improved markedly after half-time, with Joe Hart having to be at his best late on to prevent Casimero and Pepe netting all-important away goals.
Bale was frustrated not to have found a winner, especially having felt both he and Lucas Vazquez should have had penalties, but was upbeat about the 10-time champions’ chances of making the Milan finale.
“I didn’t think we had to change too much,” the attacker said of coping with Ronaldo’s absence. “I think the players, Jese and Lucas, who came in did a very good job. We looked solid, we looked a threat on the counter and we were unlucky maybe not to get the goal and a few penalties.
“It was a little bit frustrating not to be able to score, but we got a clean sheet and we go back to the Bernabeu now very confident.
Zinedine Zidane’s side certainly go into the home leg in a far better position than they did in the quarter-finals, when Wolfsburg inflicted a shock 2-0 first-leg defeat in Germany.
However, Real rallied rather than wilted on that occasion and progressed thanks to a 3-0 triumph on home turf - a result that gives them understandable confidence, albeit Bale knows City are a different calibre of opponent.
“Of course you have to play it carefully, but ultimately when we’re at home we attack a lot,” he said.
“We’ll try to keep it defensively tight as well so it will obviously be a difficult game at home, we know that. They’re a very good team.
“I think both teams are evenly matched. We’re very confident at home. We know it’ll be a difficult game, but we will be going all out to try and win it.”
Toni Kroos echoed the sentiments of team-mate Bale, underlining the belief in Madrid’s squad that they will make it to the San Siro.
“Manchester City are a good team, but we’re playing at the Bernabeu and we believe we can win the tie,” the Germany midfielder said.
“It doesn’t matter who the favourite is. The winner will be in the final. Everyone knows we’re good at home, we showed that in the quarters and we hope to do so again on Wednesday.
“We have to play well and do things like we did against Wolfsburg. If we play like that I think we’ll be in the final.”
Meanwhile City captain Vincent Kompany hopes Real Madrid feel uneasy after being held to a goalless draw.
The City captain said: “There about a million more disappointing results and 0-0, if it was an away game for me, I would not feel comfortable.
“We have a really good away record in the Champions League.
“We are still an offensive team and we are always looking to score goals.
“I wouldn’t expect us not to score for 180 minutes.
“If we don’t manage to score a goal what claims can we make for going to the final? So I expect us to score a goal, and if we do the game is going to be really interesting.”