Sir Alex Ferguson's men were beaten 2-1 in the Europa League match, one of four losses and three draws at Old Trafford in all competitions this season, but managed to progress on aggregate after winning 2-0 in Holland.
The 23-year-old, who scored in both ties, suggested that United need to learn lessons from the defeat because if points are dropped in the title race they will prove costly.
He told the Daily Mirror: "We cannot afford any draws or losses in the Premier League. We need to learn from the Ajax game because it's not a good feeling."
The league champions travel to Carrow Road to take on Norwich City on Sunday, with the Canaries in fine form having kept clean sheets in their last two home games.
However, the Mexican believes that his team feel confident about lifting the trophy once more, and believes they can overhaul rivals Manchester City.
He continued: "Now it's Norwich, which will be a difficult game.
"It's a new ground for me and we're aiming to win to keep the pressure on Manchester City. Everyone feels very confident about the Premier League. We will keep doing our best and Manchester United will never give up.
"City are a very good team and that's why there are in first place, but we will fight until the last game.
"Every player wants to defend the title. On Sunday we have a very good test and we want to win it.
"There are players coming back, which is good for the team."
The striker has been in good form of late, netting four goals in as many games and his tally for the campaign currently stands at 10.
Indeed his displays may have given Sir Alex Ferguson a selection headache ahead of the clash and he will be hoping to have forced his way into the reckoning, having had to watch Danny Welbeck and Wayne Rooney become the preferred partnership up front for most of the season.
Yet Hernandez added that he will give 100 per cent no matter if he starts the game or only plays a bit-part role.
"The goals motivate me a lot and I'm feeling good at the moment," he added.
"Whether I play one minute or 90 minutes, I will always do my best."
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