The Scot took charge in June but his reign at The Hawthorns got off to a difficult start, with just two points gained from West Brom's first four Premier League outings.
That changed at White Hart Lane at the weekend, however, as James Morrison's second-half header earned a 1-0 triumph - their first at Spurs in 30 years.
Victory lifted Irvine's men out of the bottom three and up to 16th in the early league table, and the 56-year-old is hoping for a similar standard of play in Wednesday's third-round clash.
"We were comfortable and had a good shape about us when we were in possession," he said.
"We had no need to be negative and we kept two strikers up top throughout until the end. This is a Spurs side of great quality and the concentration levels of the players has to be total - which they were.
"But it has already been said in the dressing room - that's the standard. That's the level we have set ourselves and the level we must maintain."
West Brom needed penalties to see off League Two side Oxford United in the second round following a 1-1 draw, and Irvine will be keen to avoid extra-time on Wednesday with a home clash against Burnley to come four days later.
Visitors Hull have been draw specialists in the Premier League so far this season, with three out of their five matches finishing all-square.
Steve Bruce's side looked well on course for a second league win of the campaign on Saturday when they went 2-0 up at Newcastle United, but a late brace from Papiss Cisse ensured they returned home having let two valuable points slip away.
Mohamed Diame, signed from West Ham on transfer deadline day, scored his second in as many games with a thumping effort from outside the area, and the Senegal international is hoping for more of the same as he settles into life at his new club.
"I'm very happy with my two performances so far and I feel as though I have the confidence of the manager," he told the club's official website.
"I am trying to repay him for that on the pitch and I think football is all about confidence - when you have people who believe in you, you play better.
"I'm playing as a midfielder here and I am enjoying that. I am just trying to give my best and I hope there is more to come.
"We have a lot of new players here and a lot of quality. We just need a bit of time to play together and I think we can have good hopes for the season."
Neither side has any fresh injury worries ahead of the clash, although it remains to be seen whether Irvine will give a second start in four days to Joleon Lescott, who enjoyed an impressive debut at Spurs after overcoming calf and knee injuries.
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