Stephen Rice put the Irish part-timers ahead but three goals in five second-half minutes from Roman Pavlyuchenko, Jermain Defoe and Giovani Dos Santos saw Tottenham safely home to a 3-1 victory. The one sour note for Redknapp was an injury to Aaron Lennon, which saw the England winger substituted at half-time with a groin problem.
"When we went one down we were concerned because you think maybe it's going to be one of those nights," said Redknapp.
"They played their socks off but at half-time we could have been three goals up, we were hitting the woodwork and their 'keeper was making saves.
"I thought it was a matter of time before we scored but they went and scored with their first real strike at goal and you think it's one of those nights, but we stuck a couple of chances away."
Redknapp was pleased with the energy of his side which contained youngsters such as Jake Livermore, Thomas Carroll and Kyle Walker, but he maintained that the Premier League would remain his priority this season.
Redknapp said: "We'll give it (the Europa League) our best shot and see where it takes us. Hopefully we can get through the qualifying group and then look at it again.
"The Premier League is always, for me, the biggest. It's no good at the end of the year people saying Tottenham did well, they got to the semi-final of the Europa League, but finished seventh or eighth in the league again. That's not what I want.
"I want us to have a real go in the Premier League this year and we are capable of doing that. We have fantastic players here, we play some great football, we are a good team."
On Lennon, Redknapp added: "Aaron's okay. He said his groin was a bit stiff and he didn't feel he could play on but I don't think it's too bad. We'll see when he comes in in the morning."
Source: PA
Source: PA