Midfielder Callum McGregor shot the determined visitors into the lead in the sixth minute only to see his fourth goal in seven games cancelled out by Damjan Bohar.
Skipper Charlie Mulgrew and defender Virgil van Dijk both came close before the interval and midfielder Stefan Johansen missed great chance in the second half but nevertheless the Scottish champions are in the box seat going into the second leg at Celtic Park next Tuesday night.
Deila, though, believes their task in the return game might have been that bit more easier.
The Norwegian said: "I am very pleased with the performance. The players were fantastic for 90 minutes today.
"We also created chances, 1-1 was a good result but we could have won the game. We were closer to winning than they were.
"I think we have to be more satisfied team. The away goal is vital, 1-1 is a much better result than 0-0.
"We learned a lesson at Legia, it was very early in the season and you try things but it is not just the system, they are fitter now and they know what is expected. It is getting better.
"Maribor was a very good team who are good on the counter attack but we were well organised and disciplined.
"They will be more dangerous away than at home but we have the advantage of Celtic Park.
"I have a good feeling that we are going to reach it [the group stages]."
The manager's compatriot, Johansen, inadvertently blocked a Van Dijk header on the line and missed a great chance in the second half but Deila could still smile.
He joked: "He was the best defender for Maribor. It was a fantastic save.
"I think he was very good, it was a good performance by him, he was working hard, he is a leader on the pitch and he is progressing all the time.
"He should have had a goal as well but I was pleased with him."
Maribor boss Ante Simundza insisted his side were not out of the competition despite facing an uphill task in Glasgow.
He said: "We wanted a positive result and we got one. We are still in the tie.
"Celtic were very solid in the first half but we dominated the second half and I think the draw was fair.
"The result gives an advantage to Celtic with the away goal but we did equalise very quickly and we have to be satisfied."