The striker came off the bench against the Saints at half-time with the score all square at the national stadium.
But he fired Philippe Clement’s side in front just after the hour mark following an agonising VAR wait.
The goal was awarded before the Nigerian international set up Ross McCausland to double the lead in the closing stages.
Rangers will find out their quarter-final opponents in tomorrow’s draw and Dessers says they are desperate to retain the trophy.
Speaking to Rangers TV, he said: “The mood is positive and we are happy.
“We had the feeling of winning the League Cup trophy last season and it is an amazing opportunity to win something early in the season. This was the first step, but it is a necessary step.
“It would be a dream to get to another final and win it, so we have to take it step by step and round by round, but this is a good first step.
“When you are waiting for VAR you have to be patient. It was a tough moment as we were waiting to go 1-0 up at an important moment - I was happy we got the goal.
“Ross' goal made it more comfortable. I am happy he scored but we have to kill these games off earlier.
“We have to be a bit sharper in the final third, get more chances to finish the game off. At 2-0 you become calm and let the ball do the work.”
Dessers - who has notched three goals in five games - was delighted to play his part in teeing up academy graduate McCausland to secure the Light Blues’ spot in the next round.
He believes it is a reward for all of the Northern Irish international’s hard work on the training pitch paying off.
He added: “I am pleased with my start to the season. I work hard for the team, I do the things the manager asks of me and then I know the goals will follow.
“That's the case right now, I am happy for a goal and an assist for Ross as well.
“We work a lot on finishing and Ross has the right mentality and I am glad he got rewarded.”