Rovers boss Ray McKinnon has hailed his players for “having a bash” against Celtic in the League Cup.
Midfielder Kris Commons gave a much-changed home side the lead in the 32nd minute with a stunning 20-yard drive but they suffered a few scares before Stefan Johansen’s late strike confirmed the win.
McKinnon said his side’s battling performance made it a “bittersweet” evening.
He said: “We had a few great chances, one in the first half and a couple in the second so it would have been nice had one gone in and taken it to 1-1.
“I was really pleased with the boys. This is a tough, tough place as almost everyone will find this season.
“The players worked really hard to keep us in the game to allow us to go and have a bash at them in the last 20-25 minutes.
“I felt that we had them rocking then.
“So I am really pleased with their performance. It is bittersweet night, definitely.”
Ronny Deila admitted Raith gave him a few nervy moments.
The Hoops boss said: “I am always a little bit worried. You never know in football and the cup is always like that.
“When it is 1-0 anything can happen but I think we were in good control and it was good that we got the second goal.
“When you meet a team from a lower division it is always difficult because they gave 110 per cent and sometimes it is easy to get a bit lazy, if I can say that.
“But I think our players worked really hard for 90 minutes. We kept the pressure on all the time and could have scored more.
“We kept another clean sheet which is very important.
“But every team can get one chance and they (Rovers) should get credit for hard work and defending very well.
“But I am happy with the win and we deserved it.
Deila insisted he was “not at all” disappointed that there would be no cup clash with traditional rivals Rangers again this season – the Ladbrokes Championship leaders were beaten 3-1 by St Johnstone at Ibrox on Tuesday night – and when informed of table-topping Aberdeen’s 2-0 shock defeat against Championship side Hibernian, he said: “I think it shows how difficult it is.
“It is nothing new, you never take anything for granted in football. My players were professional and did the job very well.”