In the Qualifier 1 also, Lions were inches away from the final but for a gritty knock from AB de Villiers.
After scoring 162 for seven, Lions had Hyderabad 84 for five and then 117 for six but skipper Warner carried his bat and saw his side through.
"Tonight, I think that we had a very competitive total, it was around par. 170 would have been nice as it turns out, but two (De Villiers and Warner) of the best players in the world have both got big scores against us in the last two games. Sometimes you just have to take your hat off and appreciate how good cricketers the two are. And say well played," Finch said at the post match press conference.
"It was an amazing knock, wasn't it? The way that he controlled the innings and went right through and got them home was outstanding. We have been at the receiving end of a couple of great knocks in this tournament, and it is just that one batter in every couple of games seems to get us," Finch said.
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"AB (De Villiers) in the last game and Davey (Warner) tonight. We can hold our head up very high. We played some really great cricket throughout this tournament but unfortunately we just couldn't get the world-class players out when it counted right at the end there."
tournament in Shivil. He has been outstanding for us. Anyone who can bowl with an unusual action like that and who can spin the ball both ways is a huge asset, and he has been outstanding," Finch said.
The attacking batsman also mentioned Kaushik's impact spell in last night's match, where he gave away only four runs in two overs and eventually 22 in four. His tight bowling in the middle overs put pressure on Hyderabad batsmen, keeping his side in the hunt.
"It was beautiful the way that he bowled tonight. Under pressure in a big game, to come back into the team after a few games out just shows a real lot of character and someone who hasn't had cricket given to him easily. He has had to work very hard for what he has achieved. He was great all season and I think he can play a big part going forward," he said.
"I think the way we played throughout the tournament was fantastic from the team's point of view. To finish top of the table for a franchise in their first year was fantastic. I think it's obviously disappointing that we couldn't get through to the final but the way we fought and fought...
"We had our back up against the wall a couple of times. We started off the tournament fantastic. I think we had six wins, one loss and then we had a bit of a down period but then we hit back hard and beat two outstanding teams in Kolkata and Mumbai coming into the finals," he said.