Sunderland drew 2-2 with West Ham at the Stadium of Light and remain bottom of the Premier League standings, nine points from safety.
"I thought the boys played well today and from the first minute right to the last they did everything they possibly could to get a result".
Asked further if the criticism made him question himself, he replied: "No, I just do not forget to myself that I think I have got the third or fourth-best win record in the Premier League".
Moyes said: "The supporters have been fantastic. Managers not doing well, teams not doing well, they deserve to take their frustrations out on somebody and almost always, it's the manager".
The Sunderland equaliser was a odd affair when Wahbi Khazri scored direct from a corner kick.
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The Italian snatched a 2-2 draw with 10-man West Ham moments after being introduced as an 88th-minute replacement for the injured Billy Jones, who was carried from the pitch on a stretcher while being given oxygen.
Sunderland manager David Moyes has spent the season in the relegation zone.
"It's going to be a tough task, but we've got to have the belief that we can do it".
I thought we played well today.
When you have not scored in 11 hours and 41 minutes of Premier League football, any goal is welcome and it was fitting that Sunderland's first arrived in weird style.
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"He contributed to an all-round good team performance, we needed that and I'm glad to see him", he continued. We are playing as a team, we are winning as a team, we are drawing as a team, we are losing as a team and we are conceding goals as a team.
The West Ham manager was quoted as saying by the BBC: "We are disappointed to concede a late goal".
You can listen to live radio coverage on BBC Radio London from 3pm, or alternatively, follow all the action and goals as they fly in on our live blog from 2.30pm.
In particular, Bilic absolved Randolph of blame for Khazri's freak strike. If we are talking about the goalkeeper for that goal, it's very hard for a goalkeeper.
Randolph failed to collect a high cross into the box and the ball fell to the feet of Borini, who lashed it through the covering defenders and into the net from the edge of the area. We should have used both goals as an advantage for the momentum.
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