With Rangers drawing 1-1 at Motherwell, Celtic nudged closer to their Ibrox rivals and the Hoops boss looked forward to seeing his side improve further as the title race hots up.
"It was a professional performance," Mowbray said.
"Once we got the two goals, it opened the game up and we could have scored one or two more.
"But this team will only get better.
"They have been thrown together and have only had three or four training sessions.
"Some hit the ground running some take it a little bit longer
"We have five players living in a hotel, it isn't where we want to be, it is not ideal but we will only improve from this point, I'm sure we will improve every week.
"Points will be dropped along the way and we have to keep going."
Robbie Keane missed a host of chances to score his first goal in front of the Celtic support but Mowbray believes the goals will come for the Republic of Ireland striker.
He said: "On another night he could have scored three or four goals and somewhere along the way somebody will feel the evidence of that, the quality he possesses to get in to those goal scoring positions.
"While he is frustrated tonight, somewhere along the way it will pay dividends."
Jose Goncalves was reportedly considering a dramatic U-turn on contract negotiations with Hearts, which would have probably seen him reinstated in the Jambos' starting XI, but the 24-year-old defender was not on the team sheet.
Jim Jefferies felt "let down" by Goncalves for refusing to sign a new contract.
"I was really, really confident last night," the Tynecastle boss said.
"I had expected it all to go through so I felt a bit let down.
"That shows how difficult it is but I am not giving up hope.
"I was speaking to him until nine o'clock last night, after a day at training and I thought we were very close.
"I was on the phone since I got up this morning until we left and I have been in constant contact with him.
"I am trying to understand why he is not signing.
"The club have made him a tremendous offer and the only loser is Jose, he is the one putting himself out the team.
"I'm getting the vibes that he doesn't want to play for the club and I'm trying to convince him to play.
"That's the bridge that we are trying to cross.
"He says he wants time and I will know by Friday."
Source: Team Talk
Source: Team Talk