Goals from Ashley Young and Hernandez during an improved second half ensured United head into next week's second leg at Old Trafford in full control.
But the Mexico international warned their progression was not yet assured.
"We know it is a leg of two games. We wanted a great result and thankfully we got the two goals," he told Channel Five.
"We know Ajax is a difficult team, they have history in the European cups.
"We know there is 90 minutes more.
"We can't say we are through yet."
Ajax 0 Manchester United 2: James Robson's verdict Tweet
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not bad if you considerwe had no midfield cleverley and carrick? there are better championship midfielders, and its no use saying its his first game back,the old fellow not played for months yet had to rescue the ship yet again tonight . comes back to a simple fact --no one replaced keane no one replaced scholes FACT
What you said is true
We had no midfield til Scholes came on , how many times is he going to rescue us ?
Happy Hernandez isn't gettting complacent. If we are going to win the competetion we cannot take anything for granted.
We needed to win the FA Cup in particular (as well as the Premiership and Europa Cup) in or der to have a successful season as it is the cup we have gone on without for the longest. Now we have been knocked out of that, we MUST win all the competitions we remain in!
@had a pint with bestie
Cleverley played his first game since October and Carrick did a job, as per usual. He is not a marauding attacking midfielder.
There are not better midfielders in the Championship.
Clueless.