Robert Page said Wales remained an underdog to qualify for the World Cup knockout stages after a dramatic opening day in Group B.
England quickly took control of the section beating Iran 6-2 before Wales had to rely on captain Gareth Bale to salvage a 1-1 draw with the United States.
Bale, who equalized Chris Gunter with 109 caps – the Wales men’s national team record – canceled out Timothy Weah’s first-half goal from the penalty spot eight minutes after Tim Ream had it rammed.
Wales boss Page said: “Look at the group of players England have, it was a big ask for Iran to get anything out of the game.
“England are favourites, the United States are second favourites. But there will be a few surprises along the way.
“We are just anticipating a tough game on Friday (against Iran) and that brings us to the final game against England.”
Wales’ first game at the World Cup for 64 years – the longest wait for any nation between successive appearances at the tournament – seemed to turn into a wet squib after a first half completely dominated by the United States .
Joe Rodon almost headed for his own goal and Josh Sargent hit a post before Chelsea striker Christian Pulisic freed Weah, who converted in clinical style.
Wales failed to put a glove on USA in a one-sided first half but the introduction of Kieffer Moore after the break changed the course of the competition.
Page said: “We just needed to be braver with the ball. I don’t know if it was the occasion, nervous first game.
“When you have (Aaron) Ramsey, (Harry) Wilson and (Ethan) Ampadu, you want them on the ball.
“I wanted them to be braver with the ball and we were much better in the second half.
“The lessons have been learned. We didn’t have to win the game, but it was important not to lose it.
“We scored the goal and I thought if anyone was going to win the game in the last 10 minutes it would be us.”
Page thinks the Wales side’s added depth will serve them well for the rest of the tournament.
He said: “The good thing we have, if you look on the bench now, we have Brennan (Johnson) playing in the Premier League.
“He came and had an impact, Kieffer came and had an impact.
“We have the strength in depth, I can look over my shoulder to the bench and we have players who can come in and have a real impact on games.”
Wing-back Neco Williams shared sad news after the game and dedicated the point to his grandfather, who died on Sunday.
He wrote on Twitter: “Yesterday was the hardest news I have ever had to deal with and I listened to my mum telling me that my grandfather passed away last night.
“Going from crying all day to starting a World Cup match was extremely difficult, but I got through it thanks to the support of my team-mates and my family.
“So I dedicate this match and an important point to him.”