The Hammers travel to Cardiff on Saturday on the back of a 5-0 FA Cup reverse at Nottingham Forest and 6-0 Capital One Cup capitulation at Manchester City having not won in the league since beating Fulham at the end of November.
They currently sit second-bottom of the Premier League - three points behind Saturday's opponents - and when asked if he should say sorry, he replied: "For what?
"I said before the Forest game that we had huge difficulties from a squad point of view and we would be playing a number of young players and obviously that was too much for those young players.
"The best team in the Premier League at home beat us 6-0. They beat Norwich 7-0, beat Arsenal 6-3, beat Manchester United 4-1, so in reality it is not a shock result.
"It's not a result that you want, it's a result that comes on the back of the Forest result so that builds up the pressure around you. You have to accept it and move on. I'm still here and still fighting.
"It hasn't been the best week or a number of weeks for me. Every time you lose a football match it gets more and more difficult.
"You have to stay strong as a manager and guide the players out of a difficult position. We all have to take responsibility for the situation because we all don't want to lose the football matches we've lost."
Allardyce hopes to have Andy Carroll available in south Wales and admits he may be tempted to take a risk with the striker's fitness.
"Andy is training okay and we have to talk to the lads who are looking after him on whether he's ready or not.
"We'll look at him in training today and then take a decision from there. It may be a calculated risk I'm prepared to take."
Having shipped 11 goals in their last two games, Allardyce is delighted to have James Tomkins back in the squad.
"The central defensive position has been a problem recently," he added.
"Since the central defensive partnerships have been lost through injury, we have lost our clean sheets, we have to get back to that.
"The most important thing is Cardiff. It's a massive, massive match for us. Malky Mackay did a fantastic job at Cardiff and he is a very unfortunate man to have been sacked there.
"Now Solskjaer has a great chance in the Premier League to build on his success abroad, and he'll stamp his own mark on the team."