But the Manchester United superstar, who had earlier seen his penalty saved by teenage keeper Gavin Bazunu, belatedly made his mark with two imperious headers to snatch victory.
Speaking as the Republic launched their preparations for Thursday evening’s return in Dublin, 25-year-old Anderlecht midfielder Cullen said: “He’s probably one of, if not the only, player in world football that could have scored those two goals. We know what a special player he is.
“Yes, we managed to do it for 89 minutes, but we would have much preferred to have done it for 95 or whatever it was in the end, and that’s what we’ll be looking to do on Thursday night.
“We can take a lot of encouragement from the performance we put in out there and we’ll be looking to do a similar job on Thursday night, but turn a good performance into a good result as well.”
The defeat in Portugal was Ireland’s third in as many fixtures at the start of their Group A campaign, and their qualification hopes were effectively over within six days after they could only draw with Azerbaijan and Serbia at the Aviva Stadium.
They finally registered their first win – manager Stephen Kenny’s first competitive victory at the 13th time of asking – when they beat the Azeris 3-0 in Baku last month.
The Football Association of Ireland will assess the campaign once it has drawn to a close after Sunday’s trip to Luxembourg and decide whether or not to extend Kenny’s contract, although Cullen has no doubts as to what he would like to see happen.
Asked if he thought the manager should be given a new deal, he replied: “Yes for me, 100 percent.
“The progression that the team has shown over the last year or so working together has been really enjoyable.
“I probably speak on behalf all of the lads that we’re fully behind the manager and believe in what he’s trying to do. We’re enjoying the style of football we’re playing and we’re starting to see the rewards results-wise from the performances we’ve been putting in.
“For me, it’s a pretty straightforward answer. Yes, 100 per cent, I want the manager to stay.”
Cullen’s view was backed by 20-year-old Derby midfielder Jason Knight, who added: “I’d just echo what Josh said, absolutely the same.
“On a personal level as well, he’s given me my chance, obviously with the under-21s and he’s brought me up and given me eight senior caps so far.
“I’m grateful for that and I want to see him continue and hopefully me continue underneath him.”
Bristol City winger Callum O’Dowda was added to the squad on Monday after Cardiff striker James Collins was forced to withdraw through injury.