Three points at Windsor Park will see his side go top of Group F and give them an outstanding chance of qualifying for the tournament in France next summer.
Northern Ireland fans now have real hopes of a first major tournament since the 1986 World Cup after watching their side collect 12 points from a possible 15.
Expectation levels have continued to grow with every win but with just four games remaining, O’Neill thinks his players have handled the pressure well.
He said: “They are coping fine. It is created by the media and supporters and the expectation is a good thing to have, I think.
“The players have enjoyed this campaign because as each game has gone on the expectation has increased due to the quality of their performance and the quality of their results and that’s something we want to continue.
“We have a massive game here tomorrow night, a game where three points will put us in a very, very strong position regarding qualification and the players are looking forward to the game.
“I don’t think they underestimate the challenge that lies ahead, not only tomorrow night but also in the remaining four games. We have really good senior players in this group and I don’t see any sign of them losing their focus in any shape or form.”
O’Neill appreciates that recent results have improved dramatically on previous qualifying campaigns, but insists that performances against some of the top sides in Europe in the past have not been bad.
He added: “The results have improved but I think there were a lot of good performances in the last campaign which ultimately, at times, were not rewarded and we did show ourselves a match for the likes of Portugal and Russia.
“Now what we have managed to do is consistently string results together in this campaign. We got points on the board early on which has helped us and I think momentum and confidence in the group has grown all the time.”
Watch Northern Ireland take on Romania on Saturday, June 13 from 7.30pm live on Sky Sports 5.