The hosts had the better of the chances and Hatters goalkeeper James Shea made several good saves from Marco Matias and Steven Fletcher.
With Steve Bruce not due to take charge until February 1, Agnew took charge for the first time at Hillsborough.
He said: “I thought we had the better chances in a game that towards the end opened up a bit.
“We’re disappointed not to win the game, but equally we’re still in the hat.
“The players have had a heavy Christmas period, but we went strong because we felt they could go again. Sam (Hutchinson) had a bit of a groin problem and Barry (Bannan) came off at the end with a bit of a whack.
“But defensively we looked really solid. There was a concern of too many goals being conceded, but that’s been addressed.
“The players are in a good shape and have got a good resilience about them. The only thing we lacked today was the goal - Fletcher had the chance early on and then in the second half Matias had the shot and I thought their keeper pulled a terrific save off.
“We’ll prepare for Hull next week, but once we get to Luton we’ll enjoy the game of football there and make sure we put a performance in to get us through to the next round.”
Luton manager Nathan Jones was proud of his players after earning a place in the FA Cup fourth round draw for the first time since 2013.
A resolute defensive performance, from a side who are 13 games unbeaten in League One, highlighted the capabilities of the visitors and also left questions to be asked of a lacklustre Wednesday strike-force.
Danny Hylton looked lively for the Hatters, while Elliot Lee saw a shot from distance saved as Jones’ side broke quickly on the counter.
Luton began to tire in the second half and sat further back to soak up the Wednesday pressure, earning a draw and forcing a replay at Kenilworth Road later this month.
Jones said: “I think it was deserved and I thought it was an even game between an established Championship side and us who want to get to the next level.
“We came here with a game plan and tried to be as positive as we could. We didn’t come here and park the bus and I think it could have gone either way.
“We perhaps just lacked a little bit of cutting edge in the final third, but I’m very proud of how we played because we showed that we can compete at this level.
“They had good height with all three strikers that they had but I thought we defended well.
“We treat every competition that we enter with respect. It’s not ideal having the extra game, but the chance to play at a full house back at our place is a good one.
“Without being pessimistic I don’t think we’re going to win the FA Cup. But I believe we have a wonderful chance of getting promoted, so that is the bread and butter.
“We have to take care of the replay first, but if we are to get through then we want a big carrot, a very big, expensive carrot in the next round.”