The Toffees are in the midst of a March that will see them play nine fixtures, and today's contest was their fourth game in just 11 days with an FA Cup quarter-final replay at Sunderland looming on Tuesday.

That follows consecutive midweek league fixtures against Liverpool and Arsenal, and it is understood that Moyes is particularly unhappy about the Merseyside derby fixture, which the Blues lost 3-0.

The game was moved after their local rivals reached the Carling Cup final, and Moyes felt his side could have been dealt with more sympathetically.

He said: "We have had a lot of tough games, it's been a real tough period for us.

"The Premier League have not helped us out and I have been disappointed in them. I don't think they have been fair to Everton in many ways this season."

But Moyes had no such complaints about his side's performance as they produced an outstanding second-half display, boosted by the introduction of Marouane Fellaini for Tim Cahill, to become just the third away side to win at the Liberty this season and climb to ninth in the table.

Leighton Baines' got the opener just before the hour with a superb curling free-kick after the left-back had been fouled by Ashley Williams, while striker Nikica Jelavic made the win safe as he tapped home from Fellaini's cut-back for his second goal in Everton colours.

Moyes, who had seen his side lose their two previous league games, said: "It was a really important three points. We have done well recently and not picked up points but we deserved it today against an in-form Swansea side who have a very good record at home.

"It's an excellent win, a very important three points and a good performance.

"I was not too worried, apart from the spell in the middle of the first half where Swansea had a lot of the ball.

"But I have watched Swansea a few times this season and I think that is as tough as they have had it here this season.

"Winning away is a real hard thing to do in this league even for bigger clubs. I thought we deserved it more today, we could have scored three or four and we would have deserved it."

Moyes also reserved praise for former Rangers' striker Jelavic, after seeing the Croatian get his goal after failing to convert two very good chances laid on for him by the excellent Steven Pienaar.

"He has done well," he said.

"He looks a centre-forward and he has worked hard, he missed a few chances but he kept going and got his goal in the end."

The defeat brought Swansea back down to earth after a run of three-straight wins had catapulted them up to eighth in the table, and within sight of a potential Europa League spot.

And manager Brendan Rodgers, whose side had the better of the first half without really showing a genuine cutting edge, being limited to half chances for Gylfi Sigurdsson and Danny Graham, admitted the Swans had been below their best.

"We are disappointed with the goals, we switched off on first one which led to free-kick, and the second one we did not defend as well as we normally do," he said.

"In spells we played very well, we were not at the top of our game and I have always said we had to have our foot to the floor every game or a team like Everton can come and win the game. We were just a bit off, but credit to Everton they did very well."