The holders claimed just a fourth win from 13 games of the Barclays Premier League campaign as Diego Costa's goal secured a 1-0 success at Stamford Bridge for the Blues to climb above their opponents to 15th in the table.
Jose Mourinho's position as manager had been under scrutiny after three straight league losses for the first time in Roman Abramovich's 12-year ownership
The Portuguese was subject of a first vote of confidence in that period last month.
Terry now reckons there is an opportunity for Chelsea to build upon the win, firstly at Maccabi Tel Aviv on Tuesday, before games with Tottenham, Bournemouth, Porto, Leicester, Sunderland, Watford and Manchester United before the end of 2015.
"We're delighted to win," Terry told Chelsea TV.
"Relieved as well
Picking up three points has been a really good feeling
Good performance to top it off as well.
"Hopefully we can put ourselves on a good run of games now and climb up this table.
"We can build on this now and hopefully get another win on Tuesday."
Chelsea have endured a miserable start to the season domestically, but can qualify for the Champions League knockout stages with victory in Israel, if Porto beat Dynamo Kiev.
"We have three points on the board now in the Premier League and switch focus to the Champions League again," Terry added.
"With that in mind and the importance of qualifying it's all there for everyone to see and to go and do."
Chelsea showed improvement on the losses to West Ham, Liverpool and Stoke, with Eden Hazard demonstrating glimpses of why he was footballer of the year last season.
Costa scored his fourth goal of the season after Cesc Fabregas' quick free-kick, but should have had two more and Mourinho felt his side should have won more comfortably
"Anyone who has been to the games and watched the last five, six games has seen the performances have been there," Terry added.
"(Against Norwich was) very much the same
Creating chances, shots on goal, crosses into the box
It could've been four or five
"We'll certainly take the 1-0 and we have something to build upon now."
Terry flung himself in the way of a Sebastien Bassong shot to help the Blues take just a third clean sheet of the season.
"Defensively it's great to get the clean sheet and the defenders get the credit for that, but great work from the wide men tracking back and working as a team," Terry added.
Norwich midfielder Gary O'Neil rued the defeat, after the Canaries had held out for so long.
"It's a strange one because we've worked so hard, which gives us a sense of pride," O'Neil told Norwich City TV.
"Then you reflect on the overall score being 1-0, and we go back with nothing
Coming away, doing well, but not leaving with points isn't going to keep us in leagues.
"We had a real go of it, and we're leaving disappointed because of the manner of their goal.
"Our defensive shape was good and we've carried out our game-plan well, only to switch off at a quick free-kick."
Source : PA