The Brisbane Roar coach was full of praise for his charges following their come-from-behind win over Adelaide United, who suffered their fifth loss of the A-League season
United grabbed an early lead through Osama Malik but goals either side of half time from Besart Berisha saw Brisbane claim all three points at Coopers Stadium.
Mulvey paid tribute to Adelaide and their first-half display, admitting the visitors could have found themselves well behind at the interval.
But he said was delighted with his troops' response in the second half and made special mention of Berisha's winning goal.
"I think we were very lucky, we could've been 3-1 down at half time," he said.
"I think they (Adelaide) deserve a lot of credit for the way they played. They play some good football, they try to play the game in the right way and if they had maybe a little bit more confidence maybe they would've been up 3-1 at half time.
"What I said at half time was thankfully we were still in the game at 1-1. We needed to make the most of that opportunity because we could’ve been out of sight at half time.
"But the second-half performance I have to give my lads a lot of credit because they responded to what we spoke about and it helps when you've got Bes who can score a goal on the ground with three people around him – he toe-poked it in. He got two more for us today."
Meanwhile, United coach Josep Gombau said he was concerned for the club's fans after seeing his side succumb to its fifth loss of the season.
Gombau rates the Roar as the best side in the competition and said he was pleased with United's performance, particularly in the first half, calling their effort 'brilliant'.
But, with United winless since the opening day of the season, the Spaniard also acknowledged the Reds need to start chalking up wins or run the risk of losing much more than just three points.
"Today we played against a team for me who is the best team playing football, in my opinion," he said.
"We had more of the ball than them, we created more chances than them… I am so satisfied with this. But, of course I am sad and unhappy for the result.
"Not for me, not for the players because they are believing and they know that they are working well, but for the fans and the people that come here and not see the team winning, this is my concern.
"We need to get the results. I am happy with the way that we played but we lost what is most important – the result."
Gombau scoffed at suggestions his players are unfit and suffer from second-half fadeouts, despite coughing up the lead for a fifth time this season.
United's tendency to concede after the hour mark has also been well documented with nine of the Reds' 17 goals against arriving after 60 minutes.
"I am satisfied. I don't see a problem in the fitness," he said.
"Because they (the opposition) score in the second half people think that (it is fitness), but no, this is football. I don't have this opinion that we are not fit.
"For today, for people who understand football can see that Adelaide United played a very good game and created a lot of chances. The football that we played I think that is brilliant. The first half is very good in my opinion."