The league leaders won all four of their matches in the division last month, scoring 16 goals in the process.
They also progressed to the fifth round of the Scottish Cup by beating Stranraer, but lost in the semi-finals of the League Cup against Ross County.
Deila's side, who hold a six-point lead, take on nearest challengers Aberdeen on Wednesday evening.
"Thirty days [of January] were very good," said Deila, referring to Sunday's loss against County.
"We're disappointed of course after the weekend but the team has improved lately and we have had a lot of good performances.
"In the league we have played some great games and scored a lot of goals."
Deila has bolstered his squad this month, with the arrivals of Erik Sviatchenko, Patrick Roberts and Colin Kazim-Richards, declaring himself "very happy with the window".
"Erik showed on Sunday that he's going to be a good signing for us," he said.
"Patrick comes from Manchester City with great skills. He's a talented boy and we have him for a good length of time.
"Kazim-Richards is an experienced player and he can be a leader in the group. At Feyenoord he had a lot of young players around him and we think he will suit the style of play here."
Celtic's Ronny Deila has won the Scottish Premiership manager of the month award for January.