The Foxes, third in the Premier League, are now four points clear of fifth-placed West Ham.

Victory came after Leicester reached the FA Cup final for the first time in 52 years following Sunday’s semi-final win over Southampton and Rodgers wants no distractions.

He said: “I am not thinking about the other teams, we have to think about ourselves. We can only control ourselves. There’s nothing guaranteed, we want to arrive in the top four.

“This is a team which has been evolving but I can’t ask for anything more from the players.

“Any win in the Premier League is always a really good win especially against a team who have shown a lot of good form. It was an excellent victory.

“We lost too many simple passes in the first half but you cannot take anything away from the overall performance.

“I said to the players this is the time of the season, just because they have arrived in the final, it doesn’t mean we have one foot in and one foot out. We have other commitments.”

Iheanacho missed a golden chance after just three minutes when Conor Townsend’s mistake sent him through only for Sam Johnstone to force him wide.

Mbaye Diagne missed his kick in front of goal soon after and Leicester took advantage to kill the game off.

Vardy, who had not scored in his previous 11 games, opened the scoring with his 15th of the season when he finished off Timothy Castagne’s pass after Youri Tielemans’ brilliant throughball.

Three minutes later Evans headed in from six yards against his former club to underline Leicester’s dominance.

Castagne hit the post and Matheus Pereira’s corner bounced off the top of the bar for Albion but they never threatened a comeback.

Iheanacho added a third nine minutes before the break when he collected Vardy’s pass and finished high past Johnstone.

The game was over before the break and Leicester never needed to push for another, although Iheanacho was denied a second when Johnstone saved his late free-kick.

Defeat left West Brom nine points from safety with six games left, with manager Sam Allardyce admitting there is no margin for error.

He said: “It’s (winning) five out of six to be absolutely certain (of survival) and that is a tall order. Trying to win as many games as we can starting with Aston Villa on Sunday.

“We have to bounce back from this and do our best. It was disappointing for us, especially when you know you are coming across a team like Leicester and have heard me talking about taking your chances when they arrive.

“We had ours with Mbaye and you must take that chance as it puts them on the back foot. When you miss you can often pay the price. We did because Leicester came into the game and overran us.

“The game was beyond us (at half-time) and we had to make sure we shut the back door.”