The Baggies head coach was "disappointed more than angry" after his side's late collapse against Reading, while Brian McDermott praised his player's "resilience and desire"
Reports have emerged that the west London club, who remain bottom of the Premier League despite drawing with Tottenham, have had a bid rejected for the Nigerian forward.
The 49-year-old did not comment on whether there had been a formal bid by the Rs but affirmed the Midlands club's position on their striker, insisting: "[Odemwingie] is not for sale."
The Scot was speaking after his side's 3-2 loss to Reading on Sunday, where they led 2-0 with just eight minutes remaining, before conceding three late goals to leave them with nothing.
Clarke admitted that the finale was unbelievable and rued his team's missed chances, notably from Romelu Lukaku who hit the woodwork twice before the their late capitulation.
"You never think the points are in the bag in the Premier League," he told reporters. "I thought we had good control of the game though.
"I certainly couldn't see the finish to the game that actually happened. I'm not sure [what went wrong].
"We could have been out of sight but we lost the goal on 81 minutes and for some reason we lost our shape and composure and conceded the two late goals that cost us the game.
"Sometimes football's a strange game and today was one of those days. I'm disappointed more than angry."
The Baggies seemed in control before the flurry of late action, with the hosts unable to create much of note, making Reading's winner even harder to take.
However Clarke assured fans that his players will find no trouble in bouncing back, indicating they will not dwell on the defeat.
When asked if it will be hard to lift the players, he replied: "No they are professionals.
"We've got a big game on Tuesday night (FA Cup third-round replay with QPR). We want to progress in the FA Cup and stay in as long as possible."
He also revealed that Shane Long, who missed the clash against his former club with a dead leg, is again "doubtful" for the replay with the Rs.
Reading manager Brian McDermott was naturally pleased with the outcome of the clash at the Madejski, praising his side's "resilience and desire" for the win that keeps them off the bottom of the table.
"You don't normally win games when you're two goals down with eight minutes to go," he said.
"They didn't get the third goal [and] once we scored, the crowd really got into the game and we had a chance. You have to stay in the game at this level.
"What we've got is great resilience and desire."
The win keeps the Royals in 19th place in the league table, with 16 points and 16 game remaining, but moves them to within three points of safety. The 51-year-old indicated, though, that he is not aiming for any specific final tally.
"I have no points tally in mind, no long term targets," he added. "My only target is to try and win the next game."