Walter Smith claims he welcomes the challenge from Hearts this season but was unhappy that Rangers played a part in boosting their Clydesdale Bank Premier League title credentials.
Ryan Stevenson grabbed the only goal of the game for the Jambos against Rangers at Tynecastle as they moved to within two points of the Scottish champions.
Hearts are keen to show that the title race can be a three-way fight this season, and Smith said: "It's a welcome enough challenge. Hearts, when they are on form as they are at the moment, are always going to be challengers. I don't see anything in their play that would suggest they will get any weaker as the season goes on."
He added: "It's a welcome challenge but frustrating considering the way we played. We are just a bit unhappy about the fact that we haven't managed to do better in terms of getting the result."
Next up for Hearts is a visit to Celtic Park on Wednesday before they travel to Ibrox the following midweek.
Asked whether Hearts are good enough to win in Glasgow, Smith replied: "They are steady enough and they have been doing extremely well just now.
"It's always a test for everyone. They don't lose a lot of goals. They have to come to Ibrox twice and go to Celtic Park twice so there is still a lot of football to be played. It's to Hearts' credit that they are supplying a level of competition."
Smith added: "It's not often we have come here and played as well as we did here so it's a bit frustrating when you dominate a game and end up losing it.
"We were excellent in the first half and dominated the possession. The Hearts goalkeeper had some fantastic saves to keep the scoreline at 0-0. Then a scrappy goal eventually caused us to lose the game.
"We are a big bit disappointed to lose the game playing probably better than we have done here since I came back to Rangers. It makes it doubly disappointing to play well and lose out."
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