A late Paddy McNair strike against Belarus on Tuesday night gave Northern Ireland a 1-0 win as they registered four wins from four in Group C of Euro 2020 qualifying.
Germany - also unbeaten after three games - come to Belfast in September before back-to-back games against the Netherlands and the corresponding game in Germany.
“We have to believe we can go in and win the game. It’s as simple as that,” insisted O’Neill.
“I think sometimes people think these games are a formality. They’re not. They’re never a formality for Northern Ireland.”
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He said there was every reason to be confident his squad could knock one of the big boys off their perch as he hopes his side continues to make strides forward.
O’Neill said: “We have created a points gap between ourselves and the Netherlands because of their participation in the Nations League.
“So hopefully they’ll be under a little bit more pressure.
“The belief, the energy and with the home crowd the next indication of progress of this team is to take a big scalp and certainly we have two of the biggest scalps coming to Belfast in the next few months.”
Northern Ireland has spluttered to 2-1 win in Estonia on Saturday and last night it looked as though they were heading for a scoreless draw with Belarus until McNair stepped up to deliver the crucial strike.
O’Neill’s side never seemed to run out of energy in spite of a second consecutive game in draining, humid conditions.
“It would be nice to come and win the games easily but we don’t expect that,” the manager added. “We knew we would have to go right to the wire.
“I think what these games, in particular, have proven is that the preparation has been key, to be able to do that, to have the training camps and get players to commit to that.
“A lot of the players finished their seasons on the 4th or 5th of May and they’re here on the 11th of June winning games in the 85th minute, right at the death.
“It’s a nice way to win the games, it shows great heart, great belief.”
Northern Ireland had started the game well but finished the first half on the back-foot as some loose passes allowed Belarus to push further forward.
But the momentum swung back in the second half and Northern Ireland finished the stronger side.
“At half-time, we spoke to them about needing to take more of the initiative,” O’Neill said.
“We started the game well but Belarus were coming into the game and had taken that initiative away from us.
“We felt it was necessary for us to step it up, we pressed higher in the second half and got chances early in the second half. We didn’t take them but we kept going.
“I felt our best chance was going to come from that area on the left side and ultimately it did, though possibly not in the way we imagined.
“It’s testament to the character of the team and not just the players who play but we’ve got 27 players here, not a single withdrawal and that tells you what a good squad this is. It’s a young squad, a developing squad with a lot of potential.”