In a game of few chances, it was Gary Ainsworth’s side who took their golden opportunity to claim three points.
“I think we beat ourselves a little bit today,” said Millers chief Warne after a second successive home defeat.
The goal came in the fifth minute, with Scott Kashket capitalising on a mix-up between Rotherham’s defence and goalkeeper and smashing the ball into the bottom corner past the out-of-position Daniel Iversen.
Michael Smith had the best chance to level before the break but he did not get enough contact on his header from Chiedozie Ogbene’s cross.
Rotherham reshuffled in the second half in an attempt to get back into the game but remained largely ineffective against a well-organised Wanderers side.
Kashket saw a volley acrobatically tipped away by Iversen but Rotherham rarely threatened at the other end and the 37-year-old Adebayo Akinfenwa was brought on by Wycombe for the closing stages and helped to run down the clock through five minutes of stoppage time.
“He was fantastic,” said Ainsworth. “Bayo had played two games in a week and knew he wasn’t picked but, although he had been ill in midweek, he came up on the train by himself because he didn’t want to pass anything on to the lads, got up at 11am and showed his commitment to the lads by playing his part.”
Warne, who saw four of his players booked, said: “We had a few under-performers, which is regrettable because after our midweek display, back-to-back wins would have put us possibly third with a game in hand.
“It was a good opportunity for us and, if we’re going to have a successful season, we need to get back-to-back wins.
“They got a goal early and frustrated us. We didn’t play at our best and didn’t switch the ball enough and played down the same side a bit too much.
“In fairness to Wycombe, credit to them because they came here and did a job on us. They’ve taken the points, which they fully deserve.
“Our performance just wasn’t good enough. In fairness to Wycombe, they played at Blackpool Tuesday night which isn’t a short journey for them.
“After we went a goal down, we didn’t look confident. That’s a worry and it’s our job as coaches to put the confidence in the lads.”
The Millers failed to force opposition goalkeeper Ryan Allsop into a save on a wet and miserable afternoon and Warne continued: “We’ve had a discussion with the lads. If our home form was anywhere near our away form, we’d be absolutely flying. I am making excuses and it is a young team that will get better as the season goes on. But they’ll only get better if they perform and win football matches.
“We didn’t force their keeper into any saves. The best chance was Smudge’s (Smith’s) header in the first half. He would have expected to hit the target but I felt that at all the set-pieces, we never got second contact and sometimes you need a ricochet.”
The Millers failed to match the standards they had set on Wednesday when they won 2-0 at high-flying Ipswich Town.
Warne kept faith with 10 of the 11 starters at Portman Road and rued not freshening things up more.
“It felt like we were one-dimensional. The lads looked a bit jaded. Maybe that’s my fault. I could have made more changes.
“If we could have backed up our excellence in midweek we could have shot up the table and it would have been rosy.”
Visiting manager Ainsworth had some crumbs of comfort for the Millers.
“Make no mistake, this is a strong Rotherham side. Crooks and Smith are really good players and we knew they would come on to us so we wanted to try and exploit the space behind Rotherham’s defence and use our pace and the way the goal came about showed that.
“We dealt really well with their rotation in midfield and the lads at the back were outstanding. It was a great result.”
Rotherham United: Iversen, Jones (Hastie 46), Ihiekwe, Wood (Clarke 64), Mattock, Wiles, Lindsay, Crooks, Olosunde (Morris 73), Smith, Ogbene. Unused substitutes: Ladapo, Barlaser, Price, Southern-Cooper.
Wycombe Wanderers: Allsop, Grimmer, Stewart, Charles, Jacobson, Aarons (Akinfenwa 77), Gape (Pattison 46), Thompson, Bloomfield, Wheeler, Kashket (Nnamdi Ofoborh 83). Unused substitutes: Yates, Phillips, Freeman, Parker.
Referee: N Hair (Cambridgeshire).