His team advanced after a 3-0 home victory over Viktoria Plzen, but a 2-1 defeat in the away leg left Martin unimpressed.
The manager was critical of the number of opportunities the Czech side had to score during the game.
Rafiu Durosinmi netted the first goal for Plzen just before half-time, capitalising on poor defending.
Lyall Cameron’s first goal for Rangers after the break seemed to have settled the match, but Martin was not pleased with the subsequent lack of intensity.
This allowed Svetozar Markovic to score for Plzen, securing their victory on the night.
Martin said: “I am disappointed we lost and I am disappointed with how many chances we gave up.
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“I think so much of it comes from just being so loose with the ball.
“We were playing against a team who had nothing to lose, who really committed so many numbers, four on the top line, with a heavy press.
“We played through the press a lot in the first half, got into their final third a lot, then just turned the ball over.”
His concerns were not limited to the match alone.
Cyriel Dessers almost required a stretcher before being helped off the pitch after a fall, with a potential knee injury.
Martin admitted it could be serious, pending a scan.
He said: “Yeah, it looks a nasty one, so he’s in a brace now.
“We’ll have to just wait and see over the next couple of days, have a scan and see.
“We’ll keep our fingers crossed it’s not too bad for a big man.”
Looking ahead to their forthcoming match against Club Brugge, Martin acknowledged the need for significant improvement in his team.
He said: “If we don’t show a bit more care and quality on the ball, I think we will struggle against anyone.”
He also spoke about the challenge posed by the Belgian side.
He said: “Good team, tough game, but I believe that especially at Ibrox – and I think we’ll play at home first – that can be really powerful for us.
“We have to really embrace the challenge, so I’m excited about it.
“You expect the level of competition to be good now we’re through to this stage, but we’ll be in it, and we will do our very best to win and put in a performance that we’re really happy with to set up the second leg.”
Martin’s comments suggest a desire for his team to rise to the occasion and demonstrate better care and quality in their play.
His focus is clearly on the upcoming match and the need to improve to secure further progression in the Champions League.