Maribor have been a thorn in the side of Scottish teams recently, knocking Rangers, Celtic, Aberdeen and Hibernian out of European competition over the last eight years, and reached the group stage of last year's Champions League.
"We have knocked a Champions League team out of the qualifiers and they are devastated – they had confidence, they had ego coming into this game and they had no respect for us," Gerrard told RangersTV.
"But, my players have proved over two legs we are better than Maribor, and that pleases me and that gives me great confidence going forward."
Gerrard took over at Rangers in May and has brought in 11 players as he looks to end the dominance of Glasgow rivals Celtic, who have won the league for seven successive years.
Reaching the group stage of the Europa League would also provide much-needed funds for a side that are still recovering from financial problems that saw them reformed in the bottom tier of Scottish soccer in 2012.
Former Liverpool great Gerrard, who was in charge of Liverpool's academy before taking up his first senior managerial position in Scotland, was delighted with the way his side had come together over the last month.
"We are still all new – we are still new as a team and these games are getting upon us on a Thursday, on a Sunday – it is a difficult schedule at the moment," he said.
"But these players are giving everything for me and everything for the fans and more. I can't speak highly of them enough – there are individuals there who deserve a lot of credit – Allan McGregor was a mountain for us tonight – what a man."
Rangers will next meet Russian side FC Ufa with a place in the Europa League group stage at stake.
The first match will be played at Ibrox next Thursday with the away leg in Russia on Aug. 30 -- just three days before Rangers meet Celtic in the first Old Firm derby of the season.
(Writing by Peter Rutherford in Seoul; Editing by Greg Stutchbury)
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