Player of the match Callum Robinson felt that the 0-0 draw with Portugal was proof of Ireland's progress of late as they held the eighth best team in the world in Dublin.
But the West Brom forward added that he couldn't understand why a late Matt Doherty goal was ruled out.
The visitors could afford to take a draw as they prepare for a showdown with Serbia on Sunday to decide who tops Group A, and qualifies automatically for the World Cup in Qatar.
A draw still gives the Republic the opportunity to finish third in the group with a victory over Luxembourg on Sunday.
The best opportunities at Lansdowne Road arguably fell to the visitors. Ronaldo missed both of them after the break, heading past the left post before seeing another effort curl just wide on the other side.
Doherty did have the ball in the net late on, but referee Jesus Gil Manzano had already whistled for a foul by Will Keane on keeper Rui Patricio.
"The quality they've got. It's not just about Ronaldo. There's Bruno Fernandes, (Joao) Felix came on, so we did really well," said Robinson.
"If we'd taken one or two of our chances we'd have won the game. It shows how far we've come.
"I don't know why (Doherty's goal was disallowed). I think keepers get protected a bit. Will has just put his body in, there's no harm in that, and we score the goal.
"As I said it shows how far we've come. To play against a top team and still have the courage at the back to play our football. We had numerous amount of chances where we could have won on the day."
Player of the match Callum Robinson believes Ireland had opportunities to win the match and believes the late goal was unfairly disallowed— RTÉ Soccer (@RTEsoccer) November 11, 2021
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Robinson came into the game having scored five goals in his last two appearances for Ireland. Despite not finding the back of the net against the group leaders, the West Brom striker was satisfied with his performance.
"I just like to try and get in the right areas," he continued.
"Obviously it didn't go to plan like the last game, with the hat-trick, but I just try to be a threat at all times.
"We move on. We've just proved against a top [team] that we can really compete and hopefully against Luxembourg we can get the win."