The Scot watched his side lose 2-0 at Leicester on Tuesday after goals from Islam Slimani and Jamie Vardy.
It came after a controversial few days for Moyes after footage emerged over the weekend of him telling a BBC reporter she might get a slap following a post-match interview last month.
The Scot apologised and Sunderland issued a statement backing him in his job but saying his comments were “wholly inappropriate “
Moyes said: “I think it was great to get that support from the club and I expected it
I’ve been surprised in many ways but I’ve done my job with the players, prepared them and organised them
“The world of football is a great business now, it employs an incredible amount of people, whether it be in the media or at the training grounds, and for that reason football is a big talking point.
“It (preparing for the game) was not difficult at all, I said and did all the things, prepared the players and did the same things we would do for any other game.”
Sunderland are bottom of the Premier League and eight points from safety following their 20th league defeat of the season
They go to Manchester United on Sunday with Moyes conceding their hopes of staying up are dwindling
“It’s tougher,” he said
“I really felt that to give us a real chance we would have to win one of these two away games and they both were difficult on paper.
“What I didn’t put down was a win against a Manchester United or an Arsenal or Chelsea in our remaining fixtures so in my head I know we have to win at least one of those games.”
Leicester’s victory was their fifth successive league win which lifted them to 10th and nine points above the relegation zone.
They have won all six since boss Craig Shakespeare replaced Claudio Ranieri in February but Shakespeare insisted the champions are yet to banish the threat of relegation.
He said: “No, I’m still not going to say that
Other teams are capable of going on runs and again I’ve been in football long enough to know anything can happen
We have to stay focused and move onto the next one.
“We have to make sure we’re ready for each football match
That’s my job
It (the winning run) started against Liverpool but I couldn’t have imagined it.”
Source : PA