Kyle Lafferty claimed his first competitive goal for the club following his summer move from Burnley, before Kris Boyd sealed the win from the penalty spot in the final minute of the game.

The 2-0 victory provided a positive end to what has been another difficult week for Rangers in the wake of Carlos Cuellar's departure to Aston Villa, which came hot on the heels of the Champions League defeat in Kaunas.

Smith's men have now garnered six points against Falkirk and Hearts and the Rangers boss said: "It was an important factor for us after a really disappointing European exit.

"It was important to get a couple of good results to start with and I'm pleased we have managed to do that.

"There is always a difficulty in terms of integrating new players into the team, it's not always easy to get everyone settled.

"We have a number of players just in and they have to get to know each other, play together a bit more. Hopefully, over the next four or five weeks, we will see us start to settle down.

"I felt we started the game well for the first 25 minutes and then lost our way a little bit just before and after half-time.

"We had one or two squandered opportunities but, overall, I was pleased with the way we played. The first home match is always an important one and I was pleased with how we went about the match."

Rangers are close to completing the signings of Steven Davis from Fulham, and FC Toronto's Maurice Edu, following the capture of Pedro Mendes from Portsmouth.

Mendes made his debut just 24 hours after his arrival in Glasgow.

After being thrown straight into the starting line-up against Hearts, he was named sponsor's man of the match.

Smith said: "It's an area of the field where we are a little bit short and which we have been trying to adjust to over the close season.

"There has been a bit of frustration in doing so but we are eventually getting there and hopefully that will be a good thing for us.

"I felt midfield was a position we had to improve on in terms of our overall possession of the ball.

"The thing people have to realise is, that you don't come to a club and it all appears right in front of you. Sometimes it takes longer to achieve what you want to achieve.

"We had a disappointment at the start of the season but hopefully we can come out of that and be successful in terms of our domestic campaign this year.

"We hope the addition of the midfield players will help the rest of the players overall."

A centre-half could now be Smith's final target after losing Cuellar and missing out on Cardiff defender Glenn Loovens to Celtic.

"We said we would bring in some more and there is maybe one more position we are looking to improve on. You never know," Smith said.

"It's been difficult enough trying to bring in the players we have been trying to get since the start of pre-season."

Hearts' hopes of a fightback after falling behind to Lafferty's opener were dealt a blow when substitute Saulius Mikoliunas saw red after just eight minutes on the park for two bookable offences.

He was cautioned for diving before a foul on Kenny Miller resulted in his dismissal.

Jambos boss Csaba Laszlo urged Mikoliunas to learn from his mistakes in future - but does believe the player's reputation for simulation may have played a part in the sending-off.

"Everybody must have a second chance," he insisted, before adding: "If the player gets a yellow card, then he must take some of his aggressive play back and be a little bit careful.

"This foul was not necessary. I spoke with Miko and it's very important to learn for the future.

"It's a responsibility for the players to realise that another foul could see you punished and that's what happened. We can't change it but we can learn from it."